Charge Fluctuations of a Schwarzschild Black-Hole

Abstract

In this paper we calculate charge fluctuations of a Schwarzschild black-hole of mass $M$ in thermal equilibrium with radiation and an electron-positron plasma confined within a vessel of radius R. We show that charge fluctuations are always present, even if the black-hole is neutral and the overall charge of the system vanishes. Furthermore, if $R/M >>1$ the system becomes unstable under charge fluctuations. Surprisingly enough, besides the expected thermodynamical black hole charge fluctuation that result from the fluctuations on the number of charge carriers, there are other contributions to the overall charge fluctuation of the black-hole which, against our intuition, do not depend upon the charge of the particles. We conjecture that one of the contributions is an intrinsic purely quantum mechanical fluctuation of the black-hole itself as it does not depend on any of the control parameters, namely the radius of the confining cavity nor the temperature of the system, and even not upon the mass or charge of the particles