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arXiv · 1003.0026

Entropy and Temperature From Black-Hole/Near-Horizon-CFT Duality

Leo Rodriguez·Tuna Yildirim
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Abstract

We construct a 2-dimensional CFT, in the form of a Liouville theory, in the near horizon limit of 4- and 3-dimensional black holes. The near horizon CFT assumes 2-dimensional black hole solutions first introduced by Christensen and Fulling and expanded to a greater class of black holes via Robinson and Wilczek. The 2-dimensional black holes admit a Diff($S^1$) subalgebra, which upon quantization in the horizon limit becomes Virasoro with calculable central charge. This charge and lowest Virasoro eigen-mode reproduce the correct Bekenstein-Hawking entropy of the 4- and 3-dimensional black holes via the known Cardy formula. Furthermore, the 2-dimensional CFT's energy momentum tensor is anomalous. However, In the horizon limit the energy momentum tensor becomes holomorphic equaling the Hawking flux of the 4- and 3-dimensional black holes. This encoding of both entropy and temperature provides a uniformity in the calculation of black hole thermodynamic and statistical quantities for the non local effective action approach.

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Leo Rodriguez, Tuna Yildirim. 2010-05-10. Entropy and Temperature From Black-Hole/Near-Horizon-CFT Duality. https://doi.org/10.1088/0264-9381%2F27%2F15%2F155003

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