Three-Dimensional Gravity with Conformal Scalar and Asymptotic Virasoro Algebra

Details Three-Dimensional Gravity with Conformal Scalar and Asymptotic Virasoro Algebra Three-Dimensional Gravity with Conformal Scalar and Asymptotic Virasoro Algebra

1999-10-14

arxiv.org/abs/hep-th/9910105v2

Phys.Rev. D61 (2000) 104005

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, LaTeX; v2: minor corrections

Scientific paper

10.1103/PhysRevD.61.104005

Strominger has derived the Bekenstein-Hawking entropy of the BTZ black hole using asymptotic Virasoro algebra. We apply Strominger's method to a black hole solution found by Martinez and Zanelli (MZ). This is a solution of three-dimensional gravity with a conformal scalar field. The solution is not $AdS_3$, but it is asymptotically $AdS_3$; therefore, it has the asymptotic Virasoro algebra. We compute the central charge for the theory and compares Cardy's formula with the Bekenstein-Hawking entropy. It turns out that the functional form does agree, but the overall numerical coefficient does not. This is because this approach gives the "maximum possible entropy" for the numerical coefficient.

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