我们证明了在模场变化的情况下$\mathrm{<trans\; data-src="\phi ">\phi </trans>}$黑洞热力学第一定律变成$\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="M">M（M）</trans>}<trans\; data-src="=">=</trans>\frac{\mathrm{<trans\; data-src="\kappa ">\kappa </trans>}\mathrm{<trans\; data-src="dA">数字助理</trans>}}{\mathrm{<trans\; data-src="8">8</trans>}\mathrm{<trans\; data-src="\pi ">\pi </trans>}}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="\Omega ">\Omega </trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="J">J型</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="\psi ">\psi </trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="q">q个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="\chi ">\chi </trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="p">对</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="\Sigma ">\Sigma </trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\phi ">\phi </trans>}$，其中$\mathrm{<trans\; data-src="\Sigma ">\Sigma </trans>}$是标量电荷。阿诺维特·戴斯纳-米斯纳肿块也在固定位置达到极限$\mathrm{<trans\; data-src="A">A类</trans>}$,$\mathrm{<trans\; data-src="J">J型</trans>}$,$<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="p">对</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="q">q个</trans>}<trans\; data-src=")">)</trans>$当模字段取固定值时${\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="fix">修理</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="p">对</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="q">q个</trans>}<trans\; data-src=")">)</trans>$其仅取决于电荷和磁性电荷。因此，双极黑洞使固定守恒电荷的质量最小化。我们现在可以解释极端黑洞在地平线上固定模场的事实$\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="fix">修理</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="p">对</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="q">q个</trans>}<trans\; data-src=")">)</trans>$:${\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="fix">修理</trans>}}$标量电荷消失：$\mathrm{<trans\; data-src="\Sigma ">\Sigma </trans>}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="fix">修理</trans>}}<trans\; data-src=",">,</trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="p">对</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="q">q个</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0">0</trans>}\mathrm{}$.

• 收到日期：1996年7月24日

内政部：https://doi.org/10.103/PhysRevLett.77.4992