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

Abstract

Three-dimensional black holes coupled to a self-interacting scalar field is considered. It is known that its statistical entropy $a^{\prime }la$ Strominger does $not$ 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

References in corpus (4)

• A finite action for three dimensional gravity with a minimally coupled scalar field
• Logarithmic corrections to three-dimensional black holes and de Sitter spaces
• Quantum Liouville theory and BTZ black hole entropy
• Three-dimensional black hole entropy

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