Thermodynamics of a class of non-asymptotically flat black holes in Einstein-Maxwell-Dilaton theory

Abstract

We analyse in detail the thermodynamics in the canonical and grand canonical ensembles of a class of non-asymptotically flat black holes of the Einstein-(anti) Maxwell-(anti) Dilaton theory in 4D with spherical symmetry. We present the first law of thermodynamics, the thermodynamic analysis of the system through the geometrothermodynamics methods, Weinhold, Ruppeiner, Liu-Lu-Luo-Shao and the most common, that made by the specific heat. The geometric methods show a curvature scalar identically zero, which is incompatible with the results of the analysis made by the non null specific heat, which shows that the system is thermodynamically interacting, does not possess extreme case nor phase transition. We also analyse the local and global stability of the thermodynamic system, and obtain a local and global stability for the normal case for 0<γ<1 and for other values of γ, an unstable system. The solution where γ=0 separates the class of locally and globally stable solutions from the unstable ones.

18 pages, version accepted for publication in General Relativity and Gravitation

References in corpus (10)

• Geometrothermodynamics
• Geometrothermodynamics of black holes
• Phantom Black Holes in Einstein-Maxwell-Dilaton Theory
• Thermodynamics of charged topological dilaton black holes
• Thermodynamics of rotating solutions in (n+1)-dimensional Einstein-Maxwell-dilaton gravity
• Hawking radiation of linear dilaton black holes
• Asymptotically nonflat Einstein-Born-Infeld-dilaton black holes with Liouville-type potential
• Black hole phase transitions in Hořava-Lifshitz gravity
• Magnetic Branes in $(n+1)$-dimensional Einstein-Maxwell-dilaton gravity
• Rotating Solution of Einstein-Maxwell Dilaton Gravity with Unusual Asymptotics