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

During the last twenty-five years evidence has been mounting that a blackhole surface area has a discrete spectrum. Moreover, it is widely believed that area eigenvalues are uniformally 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 4h̄ ln 3. This is the unique spacing consistent both with the areaentropy thermodynamic relation for black holes, with Boltzmann-Einstein formula in statistical physics and with Bohr’s correspondence principle. The necessity in a quantum theory of gravity was already recognized in the 1930s. However, despite the flurry of activity on this subject we still lack a complete theory of quantum gravity. It is believed that black holes may play a major role in our attempts to shed some light on the nature of a quantum theory of gravity (such as the role played by atoms in the early development of quantum mechanics). The quantization of black holes was proposed long ago in the pioneering work of Bekenstein [1]. The idea was based on the remarkable observation that the horizon area of nonextremal black holes behaves as a classical adiabatic invariant. In the spirit of Ehrenfest principle [2], any classical adiabatic invariant corresponds to a quantum entity with discrete