Holographic description of three dimensional Godel black hole

TL;DR

This paper uncovers hidden conformal symmetry in three-dimensional G"odel black holes by analyzing scalar wave equations, and proposes a holographic dual description matching black hole entropy with conformal field theory predictions.

Contribution

It demonstrates the presence of hidden conformal symmetry in G"odel black holes and establishes a holographic duality without additional conditions on scalar fields.

Findings

Radial wave equations can be rewritten as $SL(2, R)$ Casimir operators.

Holographic dual descriptions match Bekenstein-Hawking entropy with CFT Cardy formula.

Conformal symmetry exists for both extremal and non-extremal G"odel black holes.

Abstract

Three dimensional G\"{o}del black hole is a solution to Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. We have studied the hidden conformal symmetry for massive scalar field without any additional condition in the background of three dimensional non-extremal and extremal G\"{o}del black holes. This conformal symmetry is uncovered by the observation that the radial wave equations in both cases can all be rewritten in the form of $SL(2, R)$ Casimir operators through introducing two sets of conformal coordinates to write the $SL(2, R)$ generators. At last, we give the holographic dual descriptions of Bekenstein-Hawking entropies of non-extremal and extremal black holes from Cardy formula of conformal field theory.