Charge Fluctuations of a Schwarzschild Black-Hole

TL;DR

This paper investigates charge fluctuations of a Schwarzschild black hole in thermal equilibrium, revealing universal contributions from the black hole and plasma, independent of charge carriers, with implications for quantum gravity understanding.

Contribution

It demonstrates that black hole charge fluctuations have universal components unaffected by black hole mass or charge carriers, linking quantum gravity effects to observable fluctuations.

Findings

Charge fluctuations have two independent, universal contributions.

Black hole charge fluctuations are of order , near the fine structure constant.

Fluctuations do not depend on the charge of particles, suggesting a quantum gravity origin.

Abstract

In this paper, we consider charge fluctuations of a Schwarzschild black hole of mass $M$ in thermal equilibrium with a plasma consisting of photons, electrons, and positrons confined inside a cavity . The final result is astonishingly simple: charge fluctuations have two independent contributions: one that comes from the black hole itself, with no respect to the plasma, and another one that arises from the plasma; both are Universal, do not depend on the black hole mass and none of them depends on the charge of the charge carriers. They differ by a numerical factor of order one if we assume the cut-off parameter to be Planckian. Therefore, we regard them as physically identical. Interestingly enough, the black hole's charge (squared) fluctuations are of the order $\hbar$ which is not too far from the fine structure constant. The physical origin of charge fluctuations remains raises a puzzle. Since it does not depend upon the charge of the charge carriers, it cannot be regarded as resulting from the trade of charges between the black hole and the quantum fields and is truly of quantum gravity nature (albeit in a semi-classical approximation). There are at least two possible ways of interpreting our results: either charge is trapped inside the black hole and the average must be regarded over an ensemble of black-holes or eventuality charge fluctuations arise from particles crossing the Cauchy horizon $\overline{r_-} \sim \hbar/2M$ in both directions.