Quantum Geometry and Black Hole Entropy
Abstract
A ``black hole sector'' of nonperturbative canonical quantum gravity is introduced. The quantum black hole degrees of freedom are shown to be described by a ChernSimons field theory on the horizon. It is shown that the entropy of a large nonrotating black hole is proportional to its horizon area. The constant of proportionality depends upon the Immirzi parameter, which fixes the spectrum of the area operator in loop quantum gravity; an appropriate choice of this parameter gives the BekensteinHawking formula S = A/4l^{2}_{P}. With the same choice of the Immirzi parameter, this result also holds for black holes carrying electric or dilatonic charge, which are not necessarily near extremal.
 Publication:

Physical Review Letters
 Pub Date:
 February 1998
 DOI:
 10.1103/PhysRevLett.80.904
 arXiv:
 arXiv:grqc/9710007
 Bibcode:
 1998PhRvL..80..904A
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 Revtex, 8 pages, 1 figure