Entropy formula in Einstein-Maxwell-Dilaton theory and its validity for black strings

TL;DR

This paper investigates conserved charges near black hole horizons in Einstein-Maxwell-Dilaton theory, introduces a new entropy formula applicable to black strings and black holes, and addresses gauge fixing issues affecting supertranslation charges.

Contribution

It derives near horizon conserved charges, explores supertranslation modes, and validates a new entropy formula for black strings and black holes within Einstein-Maxwell-Dilaton theory.

Findings

Supertranslation charge $ ext{T}_{(0,0)}$ differs from entropy times Hawking temperature.

A gauge fixing resolves the discrepancy in supertranslation charge.

The new entropy formula $4 ext{π} ilde{J}_0^+ ilde{J}_0^-$ is valid for black strings and black holes.

Abstract

We consider near horizon fall-off conditions of stationary black holes in Einstein-Maxwell-Dilaton theory and find conserved charge conjugate to symmetry generator that preserves near horizon fall-off conditions. Subsequently, we find supertranslation, superrotation and multiple-charge modes. We apply the obtained results on a typical static dilaton black hole and on a charged rotating black string, as examples. In this case, supertranslation double-zero-mode charge $\mathcal{T}_{(0,0)}$ is not equal to black hole entropy times Hawking temperature. This may be seen as a problem but it is not, because, in Einstein-Maxwell-Dilaton theory, we have a U(1) gauge freedom and we use an appropriate gauge fixing to fix that problem. We show that new entropy formula $4 \pi \hat{J}^{+}_{0} \hat{J}^{-}_{0}$, proposed in \cite{17}, is valid for black strings as well as black holes.