Quantum Mechanics of Charged Black Holes

Details Quantum Mechanics of Charged Black Holes Quantum Mechanics of Charged Black Holes

2001-02-12

arxiv.org/abs/hep-th/0102061v2

Phys.Lett.B517:415-420,2001

Physics

High Energy Physics

High Energy Physics - Theory

5 pages, Latex. Minor changes. To appear in Phys. Lett. B

Scientific paper

10.1016/S0370-2693(01)00983-2

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.

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