Thermodynamics and Evaporation of the 2+1-D Black Hole

The properties of canonical and microcanonical ensembles of a black hole with thermal radiation and the problem of black hole evaporation in 3-D are studied. In 3-D Einstein-anti-de Sitter gravity we have two relevant mass scales, mc = 1/G, and mp = (h̄ Λ/G)1/3, which are particularly relevant for the evaporation problem. It is argued that in the ‘weak coupling’ regime Λ < (h̄G)−2, the end point of an evaporating black hole formed with an initial mass m0 > mp, is likely to be a stable remnant in equilibrium with thermal radiation. The relevance of these results for the information problem and for the issue of back reaction is discussed. In the ‘strong coupling’ regime, Λ > (h̄G)−2 a full fledged quantum gravity treatment is required. Since the total energy of thermal states in anti-de Sitter space with reflective boundary conditions at spatial infinity is bounded and conserved, the canonical and microcanonical ensembles are well defined. For a given temperature or energy black hole states are locally stable. In the weak coupling regime black hole states are more probable then pure radiation states. e-mail: [email protected]