Threedimensional quantum geometry and black holes
Abstract
We review some aspects of threedimensional quantum gravity with emphasis in the `CFT>Geometry' map that follows from the BrownHenneaux conformal algebra. The general solution to the classical equations of motion with antide Sitter boundary conditions is displayed. This solution is parametrized by two functions which become Virasoro operators after quantization. A map from the space of states to the space of classical solutions is exhibited. Some recent proposals to understand the BekensteinHawking entropy are reviewed in this context. The origin of the boundary degrees of freedom arising in 2+1 gravity is analyzed in detail using a Hamiltonian ChernSimons formalism.
 Publication:

Trends in Theoretical Physics II
 Pub Date:
 July 1999
 DOI:
 10.1063/1.59661
 arXiv:
 arXiv:hepth/9901148
 Bibcode:
 1999AIPC..484..147B
 Keywords:

 04.60.m;
 04.70.Dy;
 Quantum gravity;
 Quantum aspects of black holes evaporation thermodynamics;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 39 pages, Latex, no figures. Invited talk at the Second Meeting "Trends in Theoretical Physics", held in Buenos Aires, December, 1998. v2: References added and minor corrections. v3: An incorrect statement about the sign of the ChernSimons level erased. Extended (and in some cases modified) discussions in most sections. References added