Gravitation, the Quantum and Bohr's Correspondence Principle

The black hole combines in some sense both the“hydrogen atom” and the “black-bodyradiation” problems of quantum gravity. Thisanalogy suggests that black-hole quantization may be thekey to a quantum theory of gravity. During the last twenty-fiveyears evidence has been mounting that black-hole surfacearea is indeed quantized, with uniformally spaced areaeigenvalues. There is, however, no general agreement on the spacing of the levels. In thisessay we use Bohr's correspondence principle to providethis missing link. We conclude that the fundamental areaunit is 4h ln 3. This is the unique spacing consistent both with the area-entropythermodynamic relation for black holes, withBoltzmann-Einstein formula in statistical physics andwith Bohr's correspondence principle.