General Relativity and Gravitation

, Volume 45, Issue 11, pp 2309–2323 | Cite as

Thermodynamics of black plane solution

  • Manuel E. Rodrigues
  • Deborah F. Jardim
  • Stéphane J. M. Houndjo
  • Ratbay Myrzakulov
Research Article

Abstract

We obtain a new phantom black plane solution in \(4\)D of the Einstein–Maxwell theory coupled with a cosmological constant. We analyse their basic properties, as well as its causal structure, and obtain the extensive and intensive thermodynamic variables, as well as the specific heat and the first law. Through the specific heat and the so-called geometric methods, we analyse in detail their thermodynamic properties, the extreme and phase transition limits, as well as the local and global stabilities of the system. The normal case is shown with an extreme limit and the phantom one with a phase transition only for null mass, which is physically inaccessible. The systems present local and global stabilities for certain values of the entropy density with respect to the electric charge, for the canonical and grand canonical ensembles.

Keywords

Black plane Causal structure Thermodynamics Stability 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Manuel E. Rodrigues
    • 1
    • 2
    • 3
  • Deborah F. Jardim
    • 4
  • Stéphane J. M. Houndjo
    • 5
    • 6
  • Ratbay Myrzakulov
    • 7
  1. 1.Departamento de Física, Centro de Ciências ExatasUniversidade Federal do Espírito SantoVitóriaBrazil
  2. 2.Faculdade de FísicaUniversidade Federal do ParáBelémBrazil
  3. 3.Faculdade de Ciências Exatas e TecnologiaUniversidade Federal do ParáAbaetetubaBrazil
  4. 4.Universidade Federal dos Vales do Jequitinhonha e Mucuri, ICTMTeofilo OtoniBrazil
  5. 5.Departamento de Engenharia e Ciências Exatas, CEUNESUniversidade Federal do Espírito SantoSão MateusBrazil
  6. 6.Institut de Mathématiques et de Sciences Physiques (IMSP)Porto-NovoBénin
  7. 7.Eurasian International Center for Theoretical PhysicsL.N. Gumilyov Eurasian National UniversityAstanaKazakhstan

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