General Relativity describes the relationship between substancesgravitationTheory of interaction.Its foundation was completed by Albert Einstein in 1915 and officially published in 1916.For the first time, this theorygravitational fieldEquivalentspace-timeOfbend。[1]
In September 2022,The most accurate test of the core principle of general relativity[13]。
General relativity inAstrophysicsHas a very important application: it directly deduces some largequalityThe star will end up as a black hole - some regions in space-time are so distorted that even light cannot escape;Can formblack holeOffixed starThe minimum mass is calledchandrasekhar limit 。
General relativity also predictsGravitational waveThe existence of (Einstein's 1918 paper "On Gravitational Waves") has been confirmed by direct observation.In addition, general relativity is still moderncosmologyOfExpansion universe modelThe theoretical basis of.[2]
Spatiotemporal relationship
At the end of the 19th century, due to Newton's mechanics andmaxwell(1831-1879)Electromagnetic theorySome physicists think that "the development of physics has actually ended", but when people useGalileo transformationWhen explaining the propagation of light and other issues, we found a series of sharp contradictions, which questioned the classical concept of space and time.Einstein put forward some new ideas in physicsSpace-time view, has established the connection withlight speedCompared with the law of quasi high-speed moving objects, the theory of relativity was established.
Special relativityIt is derived on the premise of two basic assumptions:
Einstein's second theory of relativity (1916).According to this theory, gravity is determined by space——timeThe geometric effect of bending (that is, not only considering the geometry of the distance between points in space, but also considering the geometry of the distance between points in space and time) is caused by distortion, so the gravitational field affects the measurement of time and distance.[3]
Universal gravitation
General relativity: It is a theory about the essence of gravity.Einstein once tried toLaw of universal gravitationAfter several failures, he finally realized that special relativity could not accommodate the law of universal gravitation.So he willPrinciple of special relativityIt is generalized to general relativity, and also used in localInertial frameUniversal gravitation andinertia forceBased on the principle of equivalenceRiemannian Geometry A general theory of relativity that describes gravity.
Special relativity
Special relativity and general relativity: the space-time background of special relativity is straight four-dimensional space-time, while general relativity is applicable to any pseudo Riemannian space, and its space-time background is curved Riemannian space-time.
Birth background
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developing process
Einstein published a paper in 1905 to discuss the influence of gravity and acceleration on light in special relativity, and the rudiments of general relativity began to form.In 1912, Einstein published another paper on how to describe the gravitational field in geometric language.At this point, the kinematics of general relativity appeared.By 1915,Einstein field equationThe whole dynamics of general relativity was finally completed when it was published.
Solving field equations
After 1915, the development of general relativity focused on solving field equations, and the physical interpretation of solutions and the search for possible experiments and observations also accounted for a large part.But the field equation isNonlinear partial differential equationIt is difficult to find the solution, so before the computer was applied to science, only a few exact solutions were obtained.There are three most famous solutions:Schwarzschild solution Resler Northram solution, Kerr solution.[4]
Three major verifications
There are three famous experimental verifications of general relativity.In the precession of Mercury's perihelion, the remaining precession of 43 seconds per hundred years could not be explained for a long time, and was fully explained by general relativity.The bending of light in the gravitational field, the result of the calculation of general relativity is exactly twice that of Newton's theory. Eddington and Dyson's observation team used theTotal solar eclipseThe results of observation prove that the general theory of relativity is correct.and alsoGravitational redshiftAccording to the general theory of relativity, the clock in the gravitational field will slow down, so the spectral line of the light from the surface of the star to the earth will redshift, which is also confirmed in high precision.Since then, the correctness of the general theory of relativity has been widely recognized.[5]
In addition, the expansion of the universe also created another climax of general relativity.Since 1922, researchers have found that the solution to the field equation will be an expanding universe. Einstein naturally didn't believe that the universe was not static at that time, so he added aCosmological constantSo that the field equation can solve a stable universe.But this solution has two problems: theoretically, this solution is unstable and will expand or shrink once perturbed;In addition, in 1929,HubbleHe discovered that the universe is actually expanding. This experimental result made Einstein give up the cosmological constant and claimed that this was the biggest mistake in my life.
But according to the latest type ISupernovaThe expansion of the universe is accelerating.So the cosmological constant has the possibility of resurrectionDark energyIt may be explained by the cosmological constant[6]
Basic assumptions
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In brief, the two basic principles of general relativity are:
I,Principle of equivalence: The dynamic effect of inertial force field and gravitational field islocalIndiscernible[7]；
Principle of equivalence: divided intoWeak equivalence principleandStrong equivalence principleThe weak equivalence principle considers that the dynamic effects of inertial force field and gravitational field are locally indiscernible.According to the strong equivalence principle“Dynamic effect”Promote to "any physical effect".It should be emphasized that,The equivalence principle is only valid for local inertial systems，The equivalence principle of nonlocal inertial frame is not necessarily true。[7]
General relativity principleThe form of physical laws is invariant in all reference systems.The theorem isPrinciple of special relativityPromotion of.In the special theory of relativity, if we try to define the inertial system, there will be an endless cycle: generally, objects that are not subject to external forces will remain stationary orUniform linear motionThe coordinate system with constant state is the inertial system;But how to determine that the object is free from external force?The answer can only be that when an object remains stationary or moves at a constant speed in a straight line, it is not subject to external forces.Obviously, there is an inextricable loop in logic.This shows that people cannot give a strict definition of the inertial system, which is a serious defect of the special theory of relativity.In order to solve this problem, Einstein directly removed the concept of inertial frame from relativity, and replaced the "inertial frame" in the original special relativity principle with "any reference frame".[7]
General relativity is based on special relativity.If the latter is proved wrong, the whole theoretical building will collapse.
In order to understand general relativity, we must understand how mass is defined in classical mechanics.First, let's think about what quality represents in our daily life."Is it weight?" In fact, we think that mass is something that can be weighed, just as we measure it in this way: we put the object whose mass needs to be measured on a balance.What nature of mass do we use to do this?It is the fact that the earth and the measured object attract each other.This mass is called“Gravitational mass”(m1:m2=F1:F2)。We call it "gravitational" because it determines the movement of all stars and stars in the universe: the gravitational mass between the earth and the sun drives the earth to circle around the latter.
Try pushing your car on a flat surface.You can't deny that your car strongly resists the acceleration you want to give it.This is because your car has a very large mass.It is easier to move a light object than a heavy one.Mass can also be defined in another way: "It resists acceleration".This mass is called“Inertial mass”(m=F/a, note: this is not Newton's law, but a method to measure mass).
So we come to the conclusion that we can measure quality in two ways.Either we weigh it (very simple), or we measure its resistance to acceleration (the ratio of force to acceleration).
Gravitational mass and inertial mass
Many experiments have been done to measure the inertial mass and gravitational mass of the same object.All the experimental results come to the same conclusion: the inertial mass is equal to the gravitational mass (in fact, it is proportional, after adjusting the coefficient, it becomes "equal to", so as to facilitate the calculation).
Newton himself realized that this mass equivalence was caused by some reason that his theory could not explain.But he thinks this result is a simple coincidence.On the contrary, Einstein found that there was a channel to replace Newton's theory in this kind of equality.
Daily experience has verified this equivalence: two objects (one light and one heavy) will "fall" at the same speed.However, heavy objects are subject to greater gravity than light ones.So why can't it "fall" faster?Because it is more resistant to acceleration.The conclusion is that the acceleration of the object in the gravitational field is independent of its mass.Galileo was the first person to notice this phenomenon.It is important for you to understand that all objects in the gravitational field "fall at the same acceleration" is the result of the equivalence of inertial mass and gravitational mass (in classical mechanics).
Pay attention to the expression "falling".The "falling" of an object is due to the gravitational mass of the earth, which produces the gravitational field of the earth.Two objects have the same acceleration in all the same gravitational fields.Both the moon's and the sun's are accelerated at the same rate.This means that their speeds are the same in increments per second.(Acceleration is the increase in speed per second)
The Equality of Gravitational Mass and Inertial Mass
Einstein has been looking for an explanation that gravitational mass is equal to inertial mass.For this purpose, he made the third hypothesis called "the principle of equivalence".It shows that if an inertial system is uniformly accelerated relative to a Galileo system, then we can consider it (the inertial system) to be static by introducing a uniform gravitational field relative to it.
Let's examine an inertial system K ', which has a uniformly accelerated motion relative to the Galileo system.There are many objects around K and K '.This object is stationary with respect to K.So these objects have the same acceleration motion with respect to K '.This acceleration is the same for all objects, and is opposite to the acceleration direction of K 'relative to K.As we said, the acceleration of all objects in a gravitational field is the same, so its effect is equal to that K 'is static and there is a uniform gravitational field.
Therefore, if we establish the principle of equivalence, the equality of two masses of an object is only a simple deduction.This is why (quality) equivalence is an important argument supporting the principle of equivalence.
The fourth principle
By assuming that K 'is stationary andgravitational fieldExistence, we understand K 'as a Galilean system, in which we can study the laws of mechanics.Thus Einstein established his fourth principle.[8]
Theoretical content
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Principle of equivalence
Einstein put forward the "equivalence principle", that is, gravity and inertial force are equivalent.This principle is based on the equivalence of gravitational mass and inertial mass.According to the principle of equivalence, EinsteinPrinciple of special relativityIt is generalized to the principle of general relativity, that is, the form of physical laws is invariant in all reference systems.The equation of motion of the object isGeodesic lineEquation.The geodesic equation has nothing to do with the inherent properties of the object itself, but only depends on the local geometric properties of space-time.Gravity is just the expression of the local geometric properties of space-time.The existence of material mass will cause the curvature of space-time. In the curved space-time, objects still move along the shortest distance (that is, along the geodesic line -euclidean space For example, the geodesic movement of the earth in the curved space-time caused by the sun actually rotates around the sun, causing gravitational effect.Just as on the curved earth surface, if you move in a straight line, you actually walk around the great circle of the earth surface.
Geometric Basis
Gravity is the expression of local geometric properties of space-time.Although general relativity was founded by Einstein, its mathematical basis can be traced back toeuclid geometry The axiom ofEuclidThe fifth postulate (that is, parallel lines are always equidistant) has made great efforts inLobachevsky、Bordeaux、GaussianThey pointed out that EuclidFifth public establishmentIt cannot be proved by the first four public assumptions.Non Euclidean geometryGauss completed his general mathematical theory in 1827 (published in 1828). When studying the properties of surfaces, he did not use the outer space, but directly took surfaces as the research object, and created the "intrinsic" geometry of surfaces.In 1854, Gauss's studentRiemannThe intrinsic geometry of Gauss is extended to high-dimensional space, and the geometric basis of curved space of any dimension is established. It is called Riemannian geometry. Before Einstein developed general relativity, most people believed that non Euclidean geometry could not be applied to the real world.
In general relativity, the role of gravity is "geometricalized" - that is to say, the physical picture of Min's space background of special relativity plus universal gravitation in general relativity becomes the physical picture of free movement under the Riemannian space background without force (assuming no interaction such as electromagnetism), and its dynamic equation is independent of its own mass and becomes the geodesic equation.
The gravitational field equation is a very complex second-order partial differential equation with 16 independent variables.
This equation is used to describegravitational fieldAs it is a second-order nonlinear partial differential equation system, it is difficult to obtain an accurate solution. Schwarzenegger was the first to obtain an accurate solution of the equation. In the default case that the gravitational field is static spherically symmetric, he used the metric component table containing unknowns to get the Kirschner symbol and its partial derivative, and substituted them intoVacuum field equation
The second order ordinary differential equations are obtained in, and the specific expressions of metric components are obtained by solving them,Schwarzschild solution The specific form in spherical coordinates is as follows
Geometric unit system is adopted in the above gauge（
）
Represents the mass of the gravitational source.
Using the aboveGaugeThe influence of gravity on time can be obtained.
prophesy
According to general relativity, there is no gravity in the local inertial system, and one-dimensional time and three-dimensional space form a four-dimensional flatEuclidean space；In any reference system, there is gravity, which causes the curvature of spacetime, so spacetime is a four-dimensional curved non Eulerian space.Einstein found the gravitational field equation that the distribution of matter affects the geometry of space-time.The curved structure of time and space depends on the distribution of energy density and momentum density of matter in time and space, and the curved structure of time and space in turn determines the motion orbit of objects.In the case of weak gravity and small time space curvature, the prediction of general relativity is the same asNewton's law of universal gravitationandNewton's law of motionThe predictions of the two tend to be consistent;However, there is a difference between the two when the gravity is strong and the time space curve is large.Since the general theory of relativity was proposed, it has predicted the abnormal precession of Mercury perihelion, the red shift of light frequency gravityGravitational deflection of lightas well asRadar echo delayIt has been confirmed by astronomical observation or experiment.aboutPulsar binaryOur observations also provide strong evidence for the existence of gravitational waves predicted by general relativity.
Einstein put forward a revolutionary idea, that is, unlike other kinds of forces, gravity is just the result of the fact that spacetime is not flat, and earlier people assumed that spacetime is flat.An object like the earth does not move along a curved orbit because of the force called gravity. On the contrary, it moves along something in curved space that is closest to a straight path, which is called a geodesic line.A geodesic is the shortest (or longest) path between two adjacent points.In general relativity, objects always follow a straight line in four-dimensional space-time.However, it seems to us that it follows a curved path in three-dimensional space.(This is just like watching a plane flying over the ground with many mountains. Although it flies along a straight line in three-dimensional space and time, its shadow on the two-dimensional ground follows a curved path.) Another prediction of general relativity is that time seems to pass more slowly near a massive object like the earth.This is because there is a relationship between the energy of light and its frequency (the number of pulses of light per second): the greater the energy, the higher the frequency.When light travels upward from the gravitational field of the earth, it loses energy, so its frequency decreases (this indicates that the time interval between two adjacent peaks becomes larger.) In the eyes of someone above, everything that happens below seems to take longer.In 1962, people verified this prediction by using a pair of very accurate clocks installed on the top and bottom of the water tower, and found that the clock at the bottom, which was closer to the earth, walked slowly.Newton's law of motionSo that the concept of absolute position in space died, and relativity got rid of absolute time.Consider a pair of twins.If one of the children goes to live on the top of the mountain, while the other stays at sea level, the first will age faster than the second.This is calledTwin paradoxHowever, this is a paradox only for those who still have an absolute concept of time in their minds.In relativity, there is no absolute time. On the contrary, everyone has his own time measurement, which depends on where he is and how he moves.
application
General relativity was quickly recognized and appreciated by people because of its amazing verification and theoretical beauty.However, because Newton's theory of gravity has been accurate enough for most gravitational phenomena, general relativity only provides a minimal correction, and people do not need it in practice. Therefore, half a century after the establishment of general relativity, it has not received sufficient attention and has not been developed rapidly.In the 1960s, the situation changed and strong gravitational objects were discovered（neutron star）And 3KCosmic background radiation, which makes the research of general relativity flourish.General relativity is of great significance for studying the structure and evolution of celestial bodies and the structure and evolution of the universe.Formation and structure of neutron stars, black hole physics and black hole detectionGravitational radiationTheory and gravitational wave detectionBig Bang 、Quantum gravityAs well as the topological structure of large-scale space-time and other issues are being studied in depth, general relativity has become an important theoretical basis for physical research.
Experimental inspection
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Mercury perihelion precession
In 1859, astronomerLeverrier (Le Verrier) found that the observed value of Mercury perihelion precession is 38 angular seconds faster than the theoretical value calculated according to Newton's law every hundred years.He conjectured that there might be an asteroid within Mercury, and the gravity of this asteroid on Mercury caused the deviation between the two.However, after years of searching, the asteroid was never found.In 1882, S. Newcomb
After recalculation, the excess precession value of Mercury perihelion is 43 angular seconds per hundred years.He suggested that it might be caused by MercuryZodiacal lightMercury's motion is hindered by the diffuse material of.But this cannot explain why other planets have similar redundant precession.Newcomb then doubted whether gravity obeyed the inverse square law.Later, some people used electromagnetic theory to explain the abnormal phenomenon of Mercury perihelion precession, but it was unsuccessful.
In 1915, according to the general theory of relativity, Einstein regarded the movement of the planet around the sun as its movement in the solar gravitational field. Because of the curvature of the surrounding space caused by the mass of the sun, the perihelion precession of the planet every revolution is:
Where a is the long half axis of the planetary orbit, c is the speed of light, expressed in cm/s, e is the eccentricity, and T is the revolution period.For Mercury, the calculation of ε=43 ″/100 years is just in line with Newcomb's result, which solves the unsolved unsolved problem of Newton's gravity theory for many years.This result became the most powerful evidence of general relativity at that time.Mercury is the inner planet closest to the sun.The closer to the central object, the stronger the gravitational field, and the greater the curvature of space-time curvature.In addition, the eccentricity of Mercury's motion orbit is larger, so the correction value of precession is larger than that of other planets.Venus, Earth and AsteroidsIcarusThe excess precession of is also consistent with the theoretical calculation.
Bending of light in gravitational field
In 1911, Einstein discussed in his article "The Influence of Gravity on the Propagation of Light" that when light passes near the sun, it will bend due to the action of the sun's gravity.He calculated the deflection angle to be 0.83 ″, and pointed out that this phenomenon could be observed during the total solar eclipse.In 1914, the German astronomer E.F. Freundlich led a team to the Crimu Peninsula to observe the total solar eclipse in August that yearthe First World WarOutbreak, observation failed.Fortunately, because Einstein only considered the principle of equivalence at that time, the calculation result was half smaller.In 1916, Einstein recalculated the bending of light in the gravitational field according to the complete general theory of relativity.He not only considered the role of the sun's gravity, but also the space geometry deformation caused by the sun's mass. The deflection angle of the light is α=1 ″. 75R0/r, where R0 is the sun's radius and r is the distance from the light to the sun's center.
During the total solar eclipse in 1919,Royal SocietyandRoyal Astronomical SocietySent byEddington Two observation teams led by A.S. Eddington and others went to Principe in the Gulf of Guinea in West Africa and Sobra in Brazil for observation.After comparison, the observation results of the two places are 1 ″. 61 ± 0 ″. 30 and 1 ″. 98 ± 0 ″. 12 respectively.The deflection angle data measured at that time is basically consistent with Einstein's theoretical expectations.The observation accuracy is too low, and it will be interfered by other factors.People have been looking for possibilities other than total solar eclipse.Developed in the 1960sRadio astronomyIt brings hope.useradio telescopeFoundQuasar radio source。1974 and 1975a quasarThe deviation between the observed results, theoretical and observed values shall not exceed 1%.
Gravitational redshift of spectral lines
General relativity points out that the clock moves slower in a strong gravitational field, so the light emitted from the surface of a massive star to the earth will move to the red end of the spectrum.Einstein discussed this problem in his article "The Influence of Gravity on the Propagation of Light" in 1911.He uses Φ to represent the gravitational potential difference between the sun's surface and the earth, ν 0 and ν to represent the frequency of light rays on the sun's surface and when they reach the earth, so we can get:
Einstein pointed out that this result is related toFabry(C. Fabry) et al.'s observations were consistent, but Fabry thought it was due to other reasons at that time.
In 1925, W.S. Adams of Mount Wilson Observatory observedSiriusOfcompanionSirius A.This companion star is calledWhite dwarf, its density ratioplatinumTwo thousand times larger.By observing the spectral line emitted by it, the frequency shift obtained is basically consistent with the expectation of general relativity.
In 1958,Mossbauer effectWas discovered.With this effect, the resonance absorption of r ray with very high resolution can be measured.In 1959, R.V. Pound and G. Rebka first proposed the scheme of detecting gravitational frequency shift by Mossbauer effect.Then, they successfully carried out the experiment, and the results were about 5% different from the theoretical values.
useatomic clockGood results can also be obtained by measuring gravitational frequency shift.In 1971, J.C. Hafele and R.E. Keating used several cesium atomic clocks to compare the timing rates at different altitudes. One of them was placed on the ground as a reference clock, and the other several were carried by civil aviation aircraft to the sky and flew around the earth along the equator at 10000 meters.The experimental results are consistent with the theoretical predictions within 10%.1980, used by R.F.C. Vessot et alHydrogen atomic clockexperimentalize.They rocketed the hydrogen atomic clock to 10000 kilometers of space, and the difference between the results and the theoretical values was only ± 7 × 10 ^ - 5.
Radar echo delay
The bending phenomenon of light passing near a mass object can be regarded as a refraction, which is equivalent to the slowing down of the speed of light. Therefore, if the signal sent from a point in space passes near the sun, the time to reach the earth will be delayed.In 1964, I.I. Shapiro first proposed this proposal.His team has successively conducted radar experiments on Mercury, Venus and Mars, proving that the radar echo is indeed delayed.Some people began to use artificial objects as reflection targets, and the experimental accuracy was improved.Compared with the theoretical values of general relativity, the results of such experiments differ by about 1%.There are still many examples to test general relativity with astronomical observations.For example, the observation of gravitational waves andKonductraObservationHubble's law, the discovery of black holes,neutron starThe discovery of microwave background radiation and so on.Through various experimental tests, general relativity is becoming more and more convincing.However, one point should be emphasized: we can use an experiment to deny a theory, but we cannot use a limited number of experiments to finally prove a theory;An experiment with low accuracy may overturn a theory, but a series of experiments with high accuracy cannot finally confirm a theory.For the correctness of general relativity, people must take a very cautious attitude and draw reasonable conclusions strictly and carefully.
Fourth hypothesis
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Einstein's fourth hypothesis is the generalization of his first hypothesis.It can be expressed as follows: the laws of nature are the same in all systems.
It is undeniable that it sounds more "natural" to claim that the natural laws in all systems are the same than to say that only the natural laws in Galileo are the same.But we don't know whether there is a Galileo system.
This principle is called "general relativity principle"
Einstein elevator
Let's imagine an elevator falling freely inside a skyscraper. There is a fool in it.The man let his watch and handkerchief fall at the same time.What will happen?For a person outside the elevator with the earth as the reference frame, the watch, handkerchief, person and elevator are falling at the same speed.(Let's review: according to the principle of equivalence, the motion of an object in the gravitational field does not depend on its mass.) So the distance between the watch and the floor, the handkerchief and the floor, the person and the watch, and the person and the handkerchief is fixed.So for the person in the elevator, the watch and handkerchief will stay where he just threw them.
If the person gives his watch or his handkerchief a specific speed, they will move in a straight line at a constant speed.The elevator behaves like a Galileo system.However, this will not last forever.Sooner or later, the elevator will crash, and the observer outside the elevator will attend an accident funeral.
Let's do the second idealized experiment: our elevator is far away from any mass object.For example, deep in the universe.Our big fool escaped from the last accident.After several years in the hospital, he decided to return to the elevator.Suddenly a creature began to drag the elevator.Classical mechanics tells us that constant force will produce constant acceleration.(Since the mass of an object increases with the increase of speed, the constant force applied must also increase with the increase of mass in order to produce a constant acceleration. When the speed of an object approaches the speed of light, the mass of the object will tend to be infinite.) Therefore, the elevator will have an acceleration motion in the Galilean system.
Our genius fool stayed in the elevator to let his handkerchief and watch fall.People in Galileo's department outside the elevator thought that watches and handkerchiefs would hit the floor.This is because the floor collides with them (handkerchiefs and watches) due to its acceleration.In fact, people outside the elevator will find that the distance between the watch and the floor and between the handkerchief and the floor is decreasing at the same rate.On the other hand, people in the elevator will notice that his watch and handkerchief have the same acceleration, which he will attribute to the gravitational field.
The two explanations seem to be the same: one is an accelerated motion, the other is a consistent motion and gravitational field.
Let's do another experiment to prove the existence of gravitational field.A beam of light shone through the window on the opposite wall.Our two observers explained it as follows:
The people outside the elevator told us that the light shot into the elevator horizontally in a straight line at a constant speed (of course!) through the window and shone on the opposite wall.However, as the elevator is moving upward, the light irradiation point should be slightly below the incident point.
The man in the elevator said: We are in a gravitational field.Since light has no mass, it will not be affected by the gravitational field, and it will fall on the point directly opposite the incident point.
Oh!A problem has arisen.The two observers disagreed.However, the man in the elevator made a mistake.He said that light has no mass, but light has energy, and energy has a mass (remember that the mass of one joule energy is: M=E/C ^ 2), so light will have a curve path towards the floor, just as the external observer said.
Since the energy mass is very small (C ^ 2=300000000 × 300000000), this phenomenon can only be observed near a very strong gravitational field.This has been confirmed: due to the huge mass of the sun, the light will bend when approaching the sun.This experiment is the first demonstration of Einstein's theory (general relativity).
conclusion
From all these experiments, we can draw a conclusion that we can regard an acceleration system as a Galilean system by introducing a gravitational field.Extending it, we think that it is applicable to all motions, whether they are rotating (centripetal force is interpreted as gravitational field) or non-uniform acceleration motion (gravitational field that does not meet Riemann condition is converted by mathematical method).You see, general relativity is consistent with practice everywhere.
The above examples are taken from "L 'é evolution des id é es en Physique" written by Einstein and Leopold Infeld.
Physical applications
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Gravitational lens
Einstein's Cross: Four Images of the Same Celestial Body under Gravitational Lens Effect
The deflection effect of light in gravitational field is the cause of a new kind of astronomical phenomenon.When there is aMassive celestial bodyWhen the mass and relative distance of the observed celestial body are appropriate, the observer will see multiple distorted celestial body images. This effect is called gravitational lens.Affected by the system structure, size and mass distribution, the imaging can be multiple, or even form a ring called Einstein's ring, or part of the arc of the ring.The earliest gravitational lens effect was discovered in 1979, and more than 100 gravitational lenses have been discovered.Even though these images are so close to each other that they cannot be distinguished - this situation is calledMicro gravitational lens——This effect can still be measured by observing the change of total light intensity, and many micro gravitational lenses have also been found.
Gravitational wave
Artist's idea: The observation of pulsar binaries by LISA, a laser space interference gravitational wave detector, is a strong evidence indirectly confirming the existence of gravitational waves (see the section on orbital attenuation above).A considerable number of ground gravitational wave detectors have been put into operation, the most famous of which are GEO600LIGO(including three laser interference gravitational wave detectors), TAMA300 and VIRGO;The space laser interference detector LISA, which is jointly developed by the United States and Europe, is in the development stage. Its pilot test plan, LISA Pathfinder, was officially launched before the end of 2009.
American researchers announced on February 11, 2016 that they first detected gravitational waves in September 2015 using the Laser Interferometric Gravitational Wave Observatory (LIGO).Researchers announced that when two black holes collided about 1.3 billion years ago, the disturbance transmitted by the combination of two huge masses arrived at the Earth on September 14, 2015 and was detected by precision instruments on the Earth.It confirmed the prediction made by Einstein 100 years ago.
The detection of gravitational waves will greatly expand the vision of traditional observational astronomy based on electromagnetic wave observation, and people can learn the information of its wave source through the detected gravitational wave signal.The information that has never been really known may come fromblack hole、neutron starorWhite dwarfIsodense stars, possibly from someSupernovaThe explosion may even come from some imprints of the boom era at the very early stage of the birth of the universe, such as the hypotheticalCosmic string。
Black holes and others
Computer simulation of a star collapsing into a black hole and releasing gravitational waves based on the theory of general relativity The general relativity predicts the existence of a black hole, that is, when a star is dense enough, its gravity makes a region in space-time extremely distorted so that light cannot escape.In the currently widely accepted stellar evolution model, it is generally believed that the final stage of the evolution of massive stars includes the evolution of stars with about 1.4 times the solar mass into neutron stars, and stars with several to dozens of times the solar mass into stellar mass black holes.Having a mass several million to several billion times that of the sunSupermassive black holeIt is believed that they exist in the center of each galaxy legally, and their existence is generally believed to play an important role in the formation of galaxies and larger cosmic scale structures.
In astronomyCompact starOne of their most important properties is that they can efficiently convert gravitational energy into electromagnetic radiation.Stellar mass black holes orSupermassive black holeyesInterstellar gasAnd dust accretion processes are considered to be the formation mechanism of some very bright objects, and famous and diverse examples include galaxy scaleActive galactic nucleusAnd star scaleMicroquasar。In some specific cases, the accretion process will stimulate relativistic jets in these celestial bodies, which are high-energy plasma beams with jet velocity close to the speed of light and strong directionality.General relativity plays a key role in modeling these phenomena, and experimental observations also provide strong evidence to support the existence of black holes and various predictions made by general relativity.
Black hole is also one of the important targets of gravitational wave detection: the merging process of black hole binaries may radiate some of the strongest gravitational wave signals that can be received by detectors on the earth, and the chirp signal before the merging of binaries can be regarded as a“Standard candle”Thus, we can speculate the distance when merging, and further become a means to detect the expansion of the universe on a large scale.And small mass compact stars such as stellar mass black holes fall intoSupermassive black holeThe gravitational waves radiated by this process of the supermassive black hole can directly and completely restore the space-time geometric information around the supermassive black hole.
cosmology
Wilkinson Microwave Anisotropy DetectorThe temperature fluctuation of microwave background radiation in the whole day photographed by (WMAP) is based on the modern cosmological model with cosmological constantEinstein field equationThe established value of the cosmological constant has an important influence on large-scale cosmodynamics.
This modifiedEinstein field equationIt has an isotropic and uniform solution: the Friedman Lemet Robertson Volcker metric. On the basis of this solution, physicists have establishedbig bangThe model of the universe evolved from.As long as a few parameters in this model (such as the average density of matter in the universe) can be determined through astronomical observation, people can verify the correctness of this model from further experimental data.Many predictions of this model are successful, includingPrimordial nucleosynthesisThe initial abundance of chemical elements formed during the period, the large-scale structure of the universe and the "echo" left by the early cosmic temperature: cosmic microwave background radiation.
Penrose diagram of an infinite static Minkowski universe
The cosmic expansion rate obtained from astronomical observations can further estimate the total amount of matter in the universe, but the nature of matter in the universe is still a problem to be solved.It is estimated that more than 90% of the matter in the universe belongs to dark matter. They have mass (that is, they participate in gravitational interaction), but they do not participate in electromagnetic interaction, that is, they cannot be directly observed (through electromagnetic waves).There is no way to make a satisfactory description of this kind of matter in the framework of known particle physics or other theories.In addition, the observation of the red shift of distant supernovae and the measurement of the cosmic microwave background radiation show that the evolution of our universe is largely affected by the value of the cosmic constant, which determines the accelerated expansion of the universe.In other words, the accelerated expansion of the universe is determined by some form of energy with an equation of state in an unusual sense. This energy is calledDark energyIts nature is still unknown.
In the so-called inflation model, the universe once experienced a violent acceleration expansion process in the very early stage of its birth (~10-33 seconds).This hypothesis, which was put forward in the 1980s, is due to some puzzling observations that cannot be explained by classical cosmology, such as the highly isotropic cosmic microwave background radiation, and the observation of the anisotropy of the microwave background radiation is one of the evidences supporting the inflation model.However, the possible ways of inflation are also diverse, and the current observation is still unable to restrain it.A larger topic is the physics of the very early universe, which involves the classicalcosmological models PropheticBig Bang Singularity。This problem needs a completeQuantum gravityAnd this theory has not been established (see quantum gravity below).
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Causal Structure and Global Geometry
An infinite static Minkowski cosmologicalPenrose chartIn general relativity, no object with static mass can catch up with or exceed a light pulse, that is to say, event A at a certain point cannot affect position X before the light propagates from that point to any position X in space.Therefore, all light in a space-timeWorld line(Zero geodesic) contains key causal structure information about this space-time.Describing this causal structure is the Penrose Carter diagram, in which the infinite space area and time interval are "shrunk" (mathematically called compaction) through conformal transformation in the limited space-time area that can be accommodated, while the world line of light is still in theMinkowski diagramIn the same way, it is represented by a diagonal line.
Penrose and other researchers noticed the importance of causal structure and developed so-called global geometry.The objects studied in global geometry are no longerEinstein field equationA specific solution (or a family of solutions) of, but uses some relations that hold true for all geodesics, such as Raychaudhuri equation, and the nonspecific assumption of the nature of matter (usually expressed in the form of the so-called energy condition) to derive a universal conclusion.
Horizon
Under global geometry, it can be proved that there are some spacetime boundaries called event horizons, which isolate some regions in spacetime.The most famous example of this is the black hole: when the mass is compressed into a sufficiently small region in space (the correlation length isSchwarzschild radius ）, NophotonIt can escape from the inside.Since the speed of any massive particle cannot exceed the speed of light, the matter inside the black hole is also enclosed in the event horizon.However, the passage from outside the event horizon to inside the event horizon still exists, which indicates that the event horizon of a black hole, as a boundary, is not a barrier of physical properties.
The energy layer of a rotating black hole plays an important role in the process of extracting energy from the rotating black hole. Early research on black holes mainly depends on findingEinstein field equationThe famous solution includes spherically symmetricSchwarzschild solution (used to describe static black holes) and the antisymmetric Kerr solution (used to describe rotating stationary black holes, which introduces interesting properties such as the energy layer).Later research revealed more universal properties of black holes through global geometry: research shows that after a long period of time, black holes have gradually evolved into a relatively simple class of stars that can be determined by eleven parameters, including energymomentum、angular momentum, position and charge at a certain time.This property can be summarized as the hairless theorem of black holes: "black holes have no hair", that is, black holes do not have different marks like human hair styles.For example, stars passGravitational collapseThe process of forming a black hole is very complicated, but the properties of the final black hole are quite simple.
What is more worth mentioning is that black hole research has obtained a set of general laws governing the behavior of black holes, which is called black hole (thermal) mechanics. These laws andThermodynamic lawThere is a strong analogy.For example, according to the second law of black hole mechanics, the event horizon area of a black hole will never decrease spontaneously with time, which is similar to the entropy of a thermodynamic system;This law also determines that it is impossible to extract energy from a rotating black hole infinitely through classical methods (e.g. Penrose process).These strongly suggest that the mechanical law of a black hole is actually a subset of the thermodynamic law, and the surface area of a black hole is proportional to its entropy.From this assumption, we can further modify the laws of black hole mechanics.For example, because the second law of black hole mechanics isThe second law of thermodynamicsThe surface area of the black hole may also decrease if there is some other process to ensure that the total entropy of the system is increased.andThe third law of thermodynamicsIt is considered that there is no temperatureAbsolute zeroWe can further infer that black holes should also existthermal radiation；Semi classical theoretical calculations show that they do have thermal radiation. In this mechanism, the surface gravity of the black hole acts as PlanckBlackbody radiation law The role of medium temperature, this radiation is calledhawking radiation (See the quantum theory section below).
General relativity also predicts other types of event horizon models: in an expanding universe, observers may find that some regions in the past cannot be observed (so-called "particle event horizon"), while some regions in the future cannot be affected (event horizon).Even in the flatMinkowski spacetimeWhen the observer is in an accelerated reference frame, there will also be event horizons, which will also be accompanied by the Anglo radiation in the semiclassical theory.
singularity
Another common but puzzling characteristic problem of general relativity is the boundary between time and space——singularityThe occurrence of.Space time can be explored by following timelike and light like geodesics, which are the paths where photons and all other particlesfree falling movementPossible tracks in, butEinstein field equationSome of the solutions of C have a "rough edge" - this is called a space-time singularity, on which the geodesic line of time like or light like will suddenly stop, and there is no well-defined space-time geometry to describe these singularity points.It should be noted that the "singularity" may not be a "point": the "rough edge" of the solution of those field equations may not only be a "point" in the existing coordinate system, but also appear in other geometric forms (such as the "odd ring" of Kerr black hole).Singularities in general refer to curvature singularities, which means describing on these pointsSpatiotemporal curvatureFor example, the Ritchie tensor is infinite (the curvature singular point is relative to the so-called coordinate singular point, and the coordinate singular point does not belong to the category of singular point in essence: some metrics will produce infinite under a certain coordinate, but these points do not have singularity in essence, and are smooth under other suitable coordinates, and will not produce infinite curvature tensor).Famous examples of future singularities (the end of the world line) include forever staticSchwarzschild black hole The internal singularity, and the annular singularity inside the permanently rotating Kerr black hole.The Friedman Lemet Robertson Volcker metric, as well as other space-time geometry describing the universe, all have past singularities (the beginning of the world line), which is calledBig Bang Singularity, and some have future singularities（Large extrusion）。
Considering that these models are highly symmetric and thus simplified, it is easy to guess whether the appearance of singularity is just an unnatural product in the ideal state.However, the famous singularity theorem proved by global geometry points out that singularity is a general characteristic result of general relativity, and any massive entity will form singularity after gravitational collapse and reaching a specific stageExpansion universe modelSingularities also exist in.However, the content of the singularity theorem basically does not involve the nature of the singularity. These questions about determining the general structure of the singularity (such as the so-called BKL hypothesis) are the main topics of current related research.On the other hand, because a singularity wrapped in the event horizon is considered better than a "naked" singularity in terms of the destruction of physical laws, the universe supervision hypothesis was proposed, which believes that all future actual singularities (i.e. singularities formed by objects with real properties without symmetry) will be hidden within the event horizon,So as to be invisible to the external observer, that is, nature hatesNaked singularity。Although there is no actual evidence to prove this point, the results of numerical simulation support the correctness of this hypothesis.[10]
Evolution equation
every lastEinstein field equationThe solution of "is a universe". The meaning of the universe here includes not only the whole space, but also the past and the future - they are not just "snapshots" reflecting some things, but complete portraits of the space-time described.Each solution can describe the space-time geometry and material state at any time and location in its specific universe.Because of this characterization, Einstein's theory seems different from most other physical theories: most physical theories need to specify the evolution equation of a physical system (such asEllen Fest theorem）That is, if the state of a physical system at a given time is known, its evolution equation can allow to describe the past and future state of the system.The gravitational field in Einstein's theory is more different from other fields in that the former is self interacting (meaning that it is still nonlinear when no other field appears), and does not have a fixed background structure (it will evolve on a cosmic scale).
To better understandEinstein field equationThis time related partial differential equation can be written into a form that can describe the evolution of the universe with time.This form is called "3+1" decomposition, in which space-time is divided into three-dimensional space and one-dimensional time.The most famous form is called ADM form. Under this decomposition, the spatiotemporal evolution equation of general relativity has good properties: the equation has a unique solution under the given appropriate initial conditions.The "3+1" decomposition of field equations is the basis of numerical relativity.
Global and quasi local quantities
The concept of evolution equation is closely related to another aspect of general relativistic physics: in Einstein's theory, the seemingly simple concept of total mass (or energy) of a system cannot find a universal definition.The reason is that, in principle, the gravitational field does not have the energy that can be localized like other fields.
However, it is still possible to try to define the total mass of a system by other means. In classical physics, the definition of mass (or energy) can come from the conserved quantity of time shift invariance, or through the Hamiltonian form of the system.In general relativity, the following definitions of mass can be obtained from these two approaches:
*Komar mass: the conserved quantity under the time shift invariance obtained by Komar integral from the time like Killing vector, which is expressed as the total energy of a static space-time;
*ADM mass: the Hamiltonian form of general relativity is established in an asymptotically flat space-time, from which the total energy of the system is defined.
If the energy carried to infinity by gravitational waves is removed from the total mass of a system, the result is called Bondi mass at infinity of quasi light.The quality derived from these definitions is determined by Scheen andQiu ChengtongThe positive energy theorem of is proved to be positive, and momentum and angular momentum have corresponding global definitions.There are many attempts to establish the so-called quasi local quantity in this research, such as constructing the mass of an isolated system only through the physical quantity contained in the limited space region where the isolated system is located.Such attempts hope to find a better quantitative way to describe isolated systems, such as a more accurate form of the ring hypothesis.
Quantum Theory
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If general relativity is one of the two pillars of modern physics, then quantum theory is another pillar of modern physics as the basic theory for us to understand basic particles and condensed matter physics.However, how to apply the concepts in quantum theory to the framework of general relativity is still an unsolved problem.[11]
Quantum field theory
As in modern physicsParticle physicsIn the general senseQuantum field theoryIs built on a flatMinkowski spacetimeThis is a very good approximation for the description of microscopic particles in a weak gravitational field like the Earth.In some cases, the strength of the gravitational field is enough to affect the quantized matter in it, but not enough to require that the gravitational field itself is alsoquantizationFor this reason, physicists developed the quantum field theory in curved spacetime.These theories use the classical general relativity to describe the curved background spacetime, and define the quantum field theory in the generalized curved spacetime.Through this theory, it can be proved that the black hole is also releasing particles through the black body radiation, which is Hawking radiation, and may lead to the final evaporation of the black hole through this mechanism.As mentioned earlier, Stephen William Hawking radiatedblack holeIt plays a key role in the research of thermodynamics.[12]
Quantum gravity
There is no consistency between the quantized description of matter and the geometric description of spacetime, and the appearance of the singularity with infinite curvature of spacetime in general relativity (meaning that its structure becomes a micro scale), all of which require a completeQuantum gravity theoryEstablishment of.This theory needs to be able to fully describe the situation inside the black hole and the very early universe, and the gravity and related space-time geometry in it need to be described in quantized language.Although physicists have made a lot of efforts to this end, and many potential candidate theories have been developed, mankind has not yet been able to obtain a complete and self consistent quantum gravity theory.
OneCalabi-yau manifold Projection of, byString theoryAs the basis of particle physics, quantum field theory has been able to describe the other three basic interactions except gravity, but attempts to generalize gravity into the framework of quantum field theory have encountered serious problems.This attempt was successful in the low energy region. The result is an acceptable effective (quantum) field theory of gravity, but the model obtained in the high energy region is divergent (non renormalization).
One of the tentative theories trying to overcome these limitations isString theoryIn this quantum theory, the most basic unit of research is no longer a point particle, but a one-dimensional string.String theory may be able to describe the basic interactions between all particles and gravityGrand unified theoryThe cost is that it leads to abnormal characteristics such as generating six dimensional extra dimensions on the basis of three-dimensional space.In the so-called second innovation of superstring theory, people speculated thatSuperstring theory, and the unity of general relativity and supersymmetrySupergravity, can form part of a conjectured eleven dimensional model, called M theory, which is considered to be able to establish a unique definition and self consistentQuantum gravity theory。
Another attempt comes from theCanonical quantizationmethod.Applying the initial value form of general relativity (see the section of evolution equation above), the result is Wheeler Dwitt equation (its function is similar toSchrodinger equation）。Although the definition of this equation is not complete in general, with the introduction of the so-called Asiteka variable, a promising model can be obtained from this equation:Loop quantum gravity。In this theory, space is a network structure called spin network and evolves in discrete time.
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Between gravity andcosmologyGeneral relativity has become a highly successful model in the research of. So far, it has passed the test of every meaningful observation and experiment.However, even so, there is still evidence that this theory is not so perfect: the search for quantum gravity and the reality of space-time singularity still need to be solved;Support from experimental observationsdark substanceAnd the data results of the existence of dark energy are also calling for the establishment of a new kind of physics;The abnormal effect observed by Pioneer may be explained by known theories, or it may really be a prediction of the coming of new physics.However, general relativity is still full of possibilities worth exploring: mathematical relativists are seeking to understand the nature of singularities, andEinstein field equationThe basic attributes of;More and more numerical simulations such as black hole merging are being carried out by constantly updated computers;The last prediction of general relativity (gravitational waves) has been confirmed. Human beings have detected gravitational waves, and their understanding of the universe will reach a new field.More than 90 years after Einstein published his theory, general relativity is still a highly active research field.
In September 2022,The Blue Coast Observatory and the MICROSCOPE project team conducted the most accurate test so far on the weak equivalence principle (WEP) in general relativity.It is found that the acceleration difference of paired objects does not exceed about 10-15, which excludes any violation of the weak equivalence principle or deviation from the current understanding of general relativity at this level.[13]
Basic teaching plan
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generalizedPrinciple of relativityAnd the principle of equivalenceInertial reference frameAll physical laws in are the same. On this basis, Einstein made a big step forward and believed that physical laws are the same in any reference frame (including non inertial frame), which is the principle of general relativity.
Next, we will introduce another basic principle of general relativity - the principle of equivalence.
Principle of equivalence
If the spaceship is totally enclosed and the astronaut has no contact with the outside world, then he has no way to judge whether the force that causes the object to fall at a certain acceleration is gravity or inertia.In fact, not only is it a free falling experiment, but any physical process inside the spaceship cannot tell us whether the spaceship is accelerating or docking on the surface of a planet.The scene here is very similar to the scene in Galileo's ship described in the first section of this chapter.This fact reminds us that a uniform gravitational field and aUniformly accelerated motionThe reference system of is equivalent.Einstein regarded it as the second basic principle of general relativity, which is known as the principle of equivalence.
From these two basic principles, we can directly draw some unexpected conclusions.Suppose there is a spaceship in the space where gravity can be ignoredconstant acceleration , a beam of light shoots into the spaceship perpendicular to the direction of motion.Of course, the static observer outside the ship will see that the beam of light is traveling along a straight line, but the observer inside the spaceship sees a different scene with the spaceship as the reference system.In order to record the track of the beam in the spaceship, he placed some translucent screens (as shown in the figure) at equal distance in the ship. Light can pass through these screens and leave light spots on the screen.As the spaceship is advancing, the light arriving at the position of the next screen is always closer to the stern than the position of the previous display.If the spaceship doesUniform linear motionWhen the light flies between any two adjacent screens, the distance of the spaceship is equal, and the observer on the spaceship sees the light track is still a straight line (as the dotted line in the figure), although the direction of the straight line is different from the direction of the straight line seen by the stationary observer outside the ship.If the spaceship moves in a straight line with uniform acceleration, the speed of the spaceship is increasing while the light travels to the right, so the light track recorded by the observer on the ship is a parabola (as shown in the solid line in the figure).
According to the principle of equivalence, the observer in the spaceship can also completely believe that the spaceship does not accelerate, but there is a huge object in the direction of the stern. Its gravitational field affects the physical process in the spaceship.So we come to the conclusion that the gravity of an object can bend light.
Generally, the gravitational field of objects is too weak. At the beginning of the 20th century, only the light bending caused by the solar gravitational field can be observed.Due to the effect of the solar gravitational field, we may see stars behind the sun (as shown in the figure).However, the bright sky at ordinary times makes it impossible for us to observe the stars, so the best time is when there is a total solar eclipse.On May 29, 1919, there happened to be a total solar eclipse. Two British expeditions went to the Gulf of Guinea and Brazil to observe. The results fully confirmed Einstein's prediction.This is the earliest test of general relativity.
The time interval is related to the gravitational field. The existence of the gravitational field makes the time process at different locations in space different.We examine a large rotating disk (as shown in the figure).From the ground, except for the position of the rotation axis, all points on the disk are accelerating. The closer to the edge, the greater the acceleration, and the direction points to the center of the disk.It can also be seen from the ground that the closer the point is to the edge, the faster the speed is.According to special relativity, the more the same process occurs near the edge, the longer the process lasts.In other words, the time process near the edge is relatively slow.
Then the disk itself is taken as the reference system to study this phenomenon.People on the disk think that there is a gravitational field on the disk, and the direction is from the center of the disk to the edge.Since the time process near the edge is relatively slow, the people on the plate can conclude that the time process is relatively slow at the position with low gravitational potential.
There is a kind of star in the universe, which is very small in size but not small in mass. It is called dwarf star.The gravity on the surface of a dwarf star is very strong, and the gravitational potential is much lower than that on the surface of the earth.The time process on the surface of the dwarf star is relatively slow. The frequency of the emission of atoms there is lower than that of the same kind of atoms on the earth. It looks red.This phenomenon, called gravitational redshift, has been confirmed in astronomical observations.Modern technology can also verify the gravitational redshift on the earth.
The length of the rod is related to the gravitational field.When the same rod is placed at different positions on the plate, its speed of movement with the plate will be different. According to special relativity, its length will also be different. The closer it is to the edge, the shorter the rod will be.The man on the disk also observed this difference, but he took the disk as the reference system, and thought that the disk was stationary. At the same time, he also thought that there was gravity pointing to the edge of the disk at each point on the disk, so he concluded that the lower the gravitational potential, the shorter the length of the rod.
The length of the rod is related to the distribution of the gravitational field. This phenomenon reflects the fact that the actual space is not uniform due to the existence of matter, which is very different from our previous ideas.For example, the grid on a piece of cloth is neat (as shown in Figure A). If you press down with your hand, the grid will be bent (as shown in Figure B).Physics borrows the word "bending". Generally speaking, the actual space is curved due to the existence of matter.
Planets move around the sun in an elliptical orbit, sometimes closer to the sun, sometimes farther away.The huge mass of the sun bends the space around it. As a result, the major axis of the planet's orbit deflects an angle from the previous period every time the planet rotates, which is called the precession of the planet's orbit.Theoretical analysis shows that only the precession of the orbit of Mercury is significant, reaching about 0.01 ° per century.This phenomenon was discovered before the general relativity appeared, but it can't be explained, so it is actually the earliest evidence of general relativity.
General relativity and geometry Finally, we return to the rotating disk again.Special relativity tells us that only the length along the direction of motion changes, and the length perpendicular to the direction of motion does not change;If the disk is taken as the reference system, it can be said that the space scale along the gravitational direction has not changed, only the space scale perpendicular to the gravitational direction has changed.This is of great significance, because when measuring the circumference and diameter of a disk, their ratio is no longer 3.141 59..., but other values, and the sum of the internal angles of a triangle is no longer 180 °... In short, because the actual space is curved, the geometry we have learned is no longer applicable.
Geometry reflects people's understanding of space relations.Historically, people have only been exposed to relatively weak gravitational fields in relatively small spatial scales.In this case, the curvature of space can be ignored. On this basis, human developed Euclidean geometry, which reflects the reality of flat space.General relativity tells us that real space is curved, so the description of real space should be more general non Euclidean geometry.However, as a special case of non Euclidean geometry, Euclidean geometry is still correct in its scope of application and will continue to play its role.
Einstein published in 1905Special relativityLater, he began to think about how to bring gravity into the framework of special relativity.Starting from the ideal experiment of an observer in the state of free fall, he began to explore the relativity theory of gravity for eight years from 1907.After many detours and mistakes, he made a speech at the Prussian Academy of Sciences in November 1915, which was famous for itsEinstein's gravitational field equation。This equation describes how the matter in space-time affects the space-time geometry around it, and becomes the core of Einstein's general relativity [1].
Einstein's gravitational field equation is a system of second-order nonlinear partial differential equations. It is very difficult to obtain the solution of the equation mathematically.Einstein used many approximation methods to derive many initial predictions from the gravitational field equation.But soon talented astrophysicistsKarl Schwarzschild In 1916, we got the first non average exact solution of the gravitational field equation——Schwarzschild gaugeThis solution is the final stage of studying the gravitational collapse of stars, namelyblack holeThe theoretical basis of.In the same year, the research work of expanding Schwarzschild geometry to the mass with charge also began. The final result is the Resler Northrum metric, which corresponds to the static black hole with charge [2].In 1917, Einstein applied the theory of general relativity to the whole universe and created the theory of relativitycosmologyResearch field of.Considering that the theory of static universe was still widely accepted in the cosmological research at the same time, Einstein added a new constant in his gravitational field equation, which was called the cosmological constant term, to find that it was consistent with the "observation" at that time [3].However, in 1929, Hubble et al. observed that our universe was in an expansion state, and the corresponding expansion universe solution had been changed fromAlexander FriedmanFrom hisFriedman equation(also derived from Einstein's field equation)Expanding universeThe solution does not require any additional cosmological constant terms.Belgian priestLemetUsing these deconstructionsBig BangThe earliest model of[4]。Einstein later admitted that adding the cosmological constant term was the biggest mistake he made in his life [5].
At that time, general relativity still kept a sense of mystery compared with other physical theories.Because it is in harmony with the special theory of relativity and can explain many phenomena that Newton's gravity cannot explain, it is obviously better than Newton's theory.Einstein himself proved in 1915 how general relativity explainsMercuryThe process of the abnormal perihelion precession of the orbit does not require any additional parameters (the so-called "perfunctory factor") [6].Another famous experimental verification was conducted byArthur Eddington It was observed by the expedition led by Sir James on the island of Principe in Africasolar eclipseDeflection of light in solar gravitational field[7]Its deflection angle is completely consistent with the prediction of general relativity (twice the deflection angle predicted by Newton's theory). This discovery was later reported by newspapers all over the world, making Einstein's theory famous for a while [8].However, it was not until 1960 to 1975 that general relativity really entered the mainstream of theoretical physics and astrophysics. This period was called the golden age of general relativity.Physicists have gradually understood the concept of black holes, and can use the properties of astrophysicsa quasarIdentify black holes in [9].More accurateExperimental verification of general relativityIt further demonstrated the extraordinary prediction ability of general relativity [10], andRelativistic cosmologyThe prediction of the new model has also withstood the test of experimental observation.
