Quantum Mechanics of Charged Black Holes

TL;DR

This paper presents an exact quantum description of charged black holes, revealing discrete spectra for area and charge, and showing that extremal black holes are excluded from the quantum spectrum due to vacuum fluctuations.

Contribution

It provides a novel quantization scheme for charged black holes, linking their thermal properties to exact quantum operators for area and charge.

Findings

Quantization of black hole area and charge spectra.

Exclusion of extremal black holes from the quantum spectrum.

Horizon area is an adiabatic invariant.

Abstract

We quantize the spherically symmetric sector of generic charged black holes. Thermal properties are encorporated by imposing periodicity in Euclidean time, with period equal to the inverse Hawking temperature of the black hole. This leads to an exact quantization of the area (A) and charge (Q) operators. For the Reissner-Nordstr\"om black hole, $A=4\pi G \hbar (2n+p+1)$ and $Q=me$, for integers $n,p,m$. Consistency requires the fine structure constant to be quantized: $e^2/\hbar=p/m^2$. Remarkably, vacuum fluctuations exclude extremal black holes from the spectrum, while near extremal black holes are highly quantum objects. We also prove that horizon area is an adiabatic invariant.