Near Horizon Symmetry and Entropy Formula for Kerr-Newman (A)dS Black Holes

TL;DR

This paper demonstrates the universality of a specific entropy formula for Kerr-Newman (A)dS black holes in Einstein-Maxwell theory, extending previous results beyond pure Einstein gravity and addressing symmetry-related issues.

Contribution

It provides the first evidence that the entropy formula applies to Kerr-Newman (A)dS black holes in Einstein-Maxwell theory, including the resolution of symmetry generator problems.

Findings

Entropy formula holds for Kerr-Newman (A)dS black holes.

Identified supertranslation, superrotation, and multiple-charge modes.

Resolved superrotation mode problem with a new symmetry generator.

Abstract

In this paper we provide the first non-trivial evidence for universality of the entropy formula $4\pi J_{0}^{+}J_{0}^{-}$ beyond pure Einstein gravity in 4-dimensions. We consider the Einstein-Maxwell theory in the presence of cosmological constant, then write near horizon metric of the Kerr-Newman (A)dS black hole in the Gaussian null coordinate system. We consider near horizon fall-off conditions for metric and $U(1)$ gauge field. We find asymptotic combined symmetry generator, consists of diffeomorphism and $U(1)$ gauge transformation, so that it preserves fall-off conditions. Consequently, we find supertranslation, supperrotation and multiple-charge modes and then we show that the entropy formula is held for the Kerr-Newman (A)dS black hole. Supperrotation modes suffer from a problem. By introducing new combined symmetry generator, we cure that problem.