Quantum mechanics of charged black holes

Sherpa Romeo green journal. Open access article. Creative Commons Attribution License (CC BY) applies.We quantize the spherically symmetric sector of generic charged black holes. Thermal properties are incorporated 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–Nordström black hole, A = 4πG¯h(2n + p + 1) and Q= me, for integers n,p,m. Consistency requires the fine structure constant to be quantized: e2/¯h = p/m2. 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.Ye