Quantum mechanics of charged black holes

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-Nordstrom black hole, A = 4 pi Gh (2n + p + 1) and Q = me, for integers n, p,m. Consistency requires the fine structure constant to be quantized: e(2)/(h) over bar = 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. (C) 2001 Elsevier Science B.V. All rights reserved.