Bohr's Correspondence Principle and the Area Spectrum of Quantum Black Holes

During the last twenty-five years evidence has been mounting that a black-hole surface area has a discrete spectrum. Moreover, it is widely believed that area eigenvalues are uniformly spaced. There is, however, no general agreement on the spacing of the levels. In this Letter we use Bohr's correspondence principle to provide this missing link. We conclude that the area spacing of a black hole is $4ħ\ln 3$. This is the unique spacing consistent both with the area-entropy thermodynamic relation for black holes, with the Boltzmann-Einstein formula in statistical physics, and with Bohr's correspondence principle.