Building blocks of a black hole
Abstract
What is the nature of the energy spectrum of a black hole? The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As stressed long ago by Mukhanov, such eigenvalues must be exponentially degenerate with respect to the area quantum number if one is to understand black hole entropy as reflecting degeneracy of the observable states. Here we construct the black hole stationary states by means of a pair of ``creation operators'' subject to a particular simple algebra, a slight generalization of that for a pair of harmonic oscillators. This algebra reproduces the main features of the algebraic approach, in particular the equally spaced area spectrum. We then prove rigorously that the nth area eigenvalue is exactly 2^{n}fold degenerate. Thus black hole entropy qua logarithm of the number of states for a fixed horizon area is indeed proportional to that area.
 Publication:

Physical Review D
 Pub Date:
 June 2002
 DOI:
 10.1103/PhysRevD.66.024005
 arXiv:
 arXiv:grqc/0202034
 Bibcode:
 2002PhRvD..66b4005B
 Keywords:

 04.70.Dy;
 Quantum aspects of black holes evaporation thermodynamics;
 General Relativity and Quantum Cosmology;
 Astrophysics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 PhysRevTeX, 14 pages