paper

Fate of Three-Dimensional Black Holes Coupled to a Scalar Field and the Bekenstein-Hawking Entropy

arXiv:hep-th/0403089 · doi:10.1016/j.physletb.2004.07.023

Abstract

Three-dimensional black holes coupled to a self-interacting scalar field is considered. It is known that its statistical entropy $a^{'} l a$ Strominger does $n o t$ agree with the Bekenstein-Hawking (BH) entropy. However I show that, by a careful treatment of the vacuum state in the {\it canonical} ensemble with a fixed temperature, which is the same as that of the BTZ black hole without the scalar field, the BH entropy is exactly produced by the Cardy's formula. I discuss its several implications, including the fate of black holes, no-scalar-hair theorems, stability, mirror black holes, and one-loop corrections.

added discussions in Sec.5 and related references, to appear at Phys.Lett. B