Title: Charge Fluctuations of an Uncharged Black Hole Show Chinese title

Title: 带电荷的黑洞的电荷涨落

Abstract: In this paper we calculate charge fluctuations of a Schwarzschild black-hole of mass $M$ confined within a perfectly reflecting cavity of radius R in thermal equilibrium with various species of radiation and fermions . Charge conservation is constrained by a Lagrange multiplier (the chemical potential). Black hole charge fluctuations are expected owing to continuous absorption and emission of particles by the black hole. For black holes much more massive than $10^{16} g$ , these fluctuations are exponentially suppressed. For black holes lighter than this, the Schwarzschild black hole is unstable under charge fluctuations for almost every possible size of the confining vessel. The stability regime and the fluctuations are calculated through the second derivative of the entropy with respect to the charge. The expression obtained contains many puzzling terms besides the expected thermodynamical fluctuations: terms corresponding to instabilities that do not depend on the specific value of charge of the charge carriers and one of them depends on Newton's constant instead. One of the contributions to the charge fluctuations $\hbar/4\pi$ does not depend neither on number of species, nor on the the specific charge or even the size of the confining vessel. As a matter of fact, this term emerges from the second derivative of the black hole entropy alone, which means that it corresponds to a genuine quantum mechanical property of the black hole itself. Such a contribution would cause the event horizon to recede from $2M$ to $2M-T_{BH}$ or equivalently, by $(4\pi)^{-1}$ of the black hole' s Compton wave length. Similarly, a Cauchy horizon emerges at the same distance the event horizon receded. Show Chinese abstract

Abstract: 在本文中，我们计算了质量为$M$的施瓦茨希尔德黑洞，在半径为 R 的完美反射腔内与各种辐射和费米子处于热平衡时的电荷涨落。电荷守恒受到拉格朗日乘子（化学势）的约束。由于黑洞持续吸收和发射粒子，预计会出现黑洞电荷涨落。对于比$10^{16} g$大得多的黑洞，这些涨落呈指数级抑制。对于比这个质量轻的黑洞，施瓦茨希尔德黑洞在几乎所有可能大小的约束容器下都对电荷涨落不稳定。通过熵对电荷的二阶导数计算稳定区域和涨落。得到的表达式除了预期的热力学涨落外，还包含许多令人困惑的项：对应于不依赖于电荷载体特定电荷值的不稳定性项，其中一项则依赖于牛顿常数。电荷涨落的一个贡献$\hbar/4\pi$不依赖于物种数量、电荷载体的具体电荷甚至约束容器的大小。事实上，这项来自于黑洞熵的二阶导数，这意味着它对应于黑洞本身的真正量子力学性质。这样的贡献会导致事件视界从$2M$收缩到$2M-T_{BH}$或等效地，收缩$(4\pi)^{-1}$的黑洞康普顿波长。同样，当事件视界收缩相同距离时，也会出现柯西视界。