General Relativity and Gravitation

, Volume 45, Issue 7, pp 1297–1311 | Cite as

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

  • Manuel E. Rodrigues
  • Glauber Tadaiesky Marques
Research Article

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 \(0<\gamma <1\) and for other values of \(\gamma \), an unstable system. The solution where \(\gamma =0\) separates the class of locally and globally stable solutions from the unstable ones.

Keywords

Thermodynamics Black hole Phase transition 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Manuel E. Rodrigues
    • 2
    • 3
    • 1
  • Glauber Tadaiesky Marques
    • 1
  1. 1.ICIBE–LASICUniversidade Federal Rural da Amazônia-BrazilBelémBrazil
  2. 2.Centro de Ciências Exatas, Departamento de FísicaUniversidade Federal do Espírito SantoVitóriaBrazil
  3. 3.Faculdade de FísicaUniversidade Federal do ParáBelémBrazil

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