During the last twenty-five years evidence has been mounting that a black-hole surface area has a { \it discrete} spectrum. Moreover, it is widely believed that area eigenvalues are { \it uniformally} spaced. There is, however, no general agreement on the { \it 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 $4\hbar \ln 3$. This is the unique spacing consistent both with the area-entropy { \it thermodynamic} relation for black holes, with Boltzmann-Einstein formula in { \it statistical physics} and with { \it Bohr's correspondence principle}.

Categories: gr-qc hep-th quant-ph

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