Abstract
We consider the near-horizon fall-off conditions of stationary black holes in Einstein-Maxwell-Dilaton theory and find a conserved charge conjugate to the symmetry generator that preserves these conditions. Subsequently, we find supertranslation, superrotation, and multiple-charge modes and calculate them for two spacial examples: a typical static dilaton black hole and a charged rotating black string. In Einstein-Maxwell-Dilaton theory, the supertranslation double-zero-mode charge ${\mathcal{T}}_{(0,0)}$ is not equal to the product of the black hole entropy and the Hawking temperature. This may be seen as a problem, but it is not. There is a $U(1)$ gauge freedom, and we use gauge fixing to fix the problem. We show that the new entropy formula $4\ensuremath{\pi}{\stackrel{^}{J}}_{0}^{+}{\stackrel{^}{J}}_{0}^{\ensuremath{-}}$, proposed by Gonzalez et al. [EPJ Web Conf. 168, 01009 (2018)], is valid for black strings as well as black holes.
Highlights
The Einstein-Maxwell-dilaton (EMD) theory originating from a low-energy limit of string theory allows for black holes that have mass, rotation, charge, and scalar hair [1]
In order to investigate the universality of the above entropy formula, here we study the near-horizon fall-off conditions of stationary black holes in EMD theory
The equations of motion imply that the surface gravity κ and first-order term of the timelike component of the Uð1Þ gauge field Aðv0Þ have to be constants for stationary black holes
Summary
The Einstein-Maxwell-dilaton (EMD) theory originating from a low-energy limit of string theory allows for black holes that have mass, rotation, charge, and scalar hair [1]. Rotating solutions of EMD theory with a Liouville-type potential in four and (n þ 1) dimensions with flat horizons have been studied, respectively, in Refs. In order to investigate the universality of the above entropy formula, here we study the near-horizon fall-off conditions of stationary black holes in EMD theory. We show that the above new entropy formula is valid for black hole solutions, but that it works correctly for black string solutions. For this propose, we use the covariant phase space method for obtaining conserved charges in EMD theory. We obtain supertranslation, superrotation, and multiple-charge modes
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