Asymptotic symmetries on Kerr--Newman horizon without anomaly of diffeomorphism invariance

TL;DR

This paper investigates the asymptotic symmetries of Kerr--Newman black hole horizons, demonstrating the absence of diffeomorphism anomalies and discussing implications for black hole microstates and thermodynamics.

Contribution

It derives universal asymptotic Killing vectors for Kerr--Newman horizons and shows the central charge vanishes, indicating no anomaly in the symmetry algebra.

Findings

Asymptotic Killing vectors are universal for Killing horizons.

The phase space size varies for extreme black holes based on global structure.

Central charge in the symmetry algebra is zero, implying no diffeomorphism anomaly.

Abstract

We analyze asymptotic symmetries on the Killing horizon of the four-dimensional Kerr--Newman black hole. We first derive the asymptotic Killing vectors on the Killing horizon, which describe the asymptotic symmetries, and find that the general form of these asymptotic Killing vectors is the universal one possessed by arbitrary Killing horizons. We then construct the phase space associated with the asymptotic symmetries. It is shown that the phase space of an extreme black hole either has the size comparable with a non-extreme black hole, or is small enough to exclude degeneracy, depending on whether or not the global structure of a Killing horizon particular to an extreme black hole is respected. We also show that the central charge in the Poisson brackets algebra of these asymptotic symmetries vanishes, which implies that there is not an anomaly of diffeomorphism invariance. By taking into account other results in the literature, we argue that the vanishing central charge on a black hole horizon, in an effective theory, looks consistent with the thermal feature of a black hole. We furthermore argue that the vanishing central charge implies that there are infinitely many classical configurations that are associated with the same macroscopic state, while these configurations are distinguished physically.