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

TL;DR

This paper constructs a 2D conformal field theory near black hole horizons that accurately reproduces black hole entropy and temperature, offering a unified approach to black hole thermodynamics via holographic duality.

Contribution

It introduces a Liouville theory-based 2D CFT in the near horizon limit that captures black hole entropy and temperature through Virasoro algebra and Cardy formula.

Findings

Reproduces Bekenstein-Hawking entropy using Virasoro algebra.

Shows the energy-momentum tensor matches Hawking flux in the horizon limit.

Provides a unified framework for black hole thermodynamics.

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.