Thermodynamic geodesics of a Reissner Nordström black hole

  • Christine Farrugia
  • Joseph Sultana
Research Article


Starting from a Geometrothermodynamics metric for the space of thermodynamic equilibrium states in the mass representation, we use numerical techniques to analyse the thermodynamic geodesics of a supermassive Reissner Nordström black hole in isolation. Appropriate constraints are obtained by taking into account the processes of Hawking radiation and Schwinger pair-production. We model the black hole in line with the work of Hiscock and Weems (Phys Rev D 41:1142–1151, 1990). It can be deduced that the relation which the geodesics establish between the entropy S and electric charge Q of the black hole extremises changes in the black hole’s mass. Indeed, the expression for the entropy of an extremal black hole is an exact solution to the geodesic equation. We also find that in certain cases, the geodesics describe the evolution brought about by the constant emission of Hawking radiation and charged-particle pairs.


Reissner Nordström black hole Geometrothermodynamics Geodesics Hawking radiation Schwinger mechanism 



C. F. would like to thank Prof. H. Quevedo of the Universidad Nacional Autónoma de México, Prof. J. Muscat (Department of Mathematics, University of Malta) and Prof. K. Zarb Adami (Institute of Space Sciences and Astronomy, University of Malta).


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of MaltaMsidaMalta

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