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

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.

15 pages. arXiv admin note: substantial text overlap with arXiv:1802.04665