General Hidden Conformal Symmetry of 4D Kerr-Newman and 5D Kerr Black Holes

TL;DR

This paper demonstrates the existence of a general hidden conformal symmetry in four-dimensional Kerr-Newman and five-dimensional Kerr black holes, supporting dual CFT descriptions and matching entropy and Green's functions.

Contribution

It introduces a unified CFT dual framework for non-extremal Kerr-Newman black holes and extends the analysis to five-dimensional Kerr black holes, revealing consistent hidden conformal symmetries.

Findings

Existence of hidden conformal symmetry in non-extremal Kerr-Newman black holes.

Reproduction of Bekenstein-Hawking entropy via Cardy formula.

Matching retarded Green's functions with CFT predictions.

Abstract

There are two known CFT duals, namely the J-picture and the Q-picture, for a four-dimensional Kerr-Newman black hole, corresponding to the angular momentum $J$ and the electric charge $Q$ respectively. In our recent study we found a one-parameter class of CFT duals for extremal Kerr-Newman black hole, connecting these two pictures. In this paper we study these novel CFT duals for the generic non-extremal Kerr-Newman black hole. We investigate the hidden conformal symmetry in the low frequency scattering off Kerr-Newman black hole, from which the dual temperatures could be read. We find that there still exists a hidden conformal symmetry for a general CFT dual. We reproduce the correct Bekenstein-Hawking entropy from the Cardy formula, assuming the form of the central charge being invariant. Moreover we compute the retarded Green's function in the general CFT dual picture and find it is in good match with the CFT prediction. Furthermore we discuss the hidden conformal symmetries of the five dimensional Kerr black hole and obtain the similar evidence to support the general dual CFT pictures.