Geometrothermodynamics of the Kehagias–Sfetsos black hole

W. Janke, D.A. Johnston, Ralph Kenna

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Abstract

The application of information geometric ideas to statistical mechanics using a metric on the space of states, as pioneered by Ruppeiner and Weinhold, has proved to be a useful alternative approach to characterizing phase transitions. Some puzzling anomalies become apparent, however, when these methods are applied to the study of black hole thermodynamics. A possible resolution was suggested by Quevedo et al who emphasized the importance of Legendre invariance in thermodynamic metrics. They found physically consistent results for various black holes when using a Legendre invariant metric, which agreed with a direct determination of the properties of phase transitions from the specific heat. Recently, information geometric methods have been employed by Wei et al to study the Kehagias–Sfetsos (KS) black hole in Hořava–Lifshitz gravity. The formalism suggests that a coupling parameter in this theory plays a role analogous to the charge in Reissner–Nordström black holes or angular momentum in the Kerr black hole and the calculation of the specific heat shows a singularity which may be interpreted as a phase transition. When the curvature of the Ruppeiner metric is calculated for such a theory, it does not, however, show a singularity at the phase transition point. We show that the curvature of a particular Legendre invariant ('Quevedo') metric for the KS black hole is singular at the phase transition point. We contrast the results for the Ruppeiner, Weinhold and Quevedo metrics and in the latter case investigate the consistency of taking either the entropy or mass as the thermodynamic potential.
Original languageEnglish
Pages (from-to)425206
JournalJournal of Physics A: Mathematical and Theoretical
Volume43
Issue number42
DOIs
Publication statusPublished - 2010

Fingerprint

Black Holes
Phase Transition
Phase transitions
Legendre
Metric
Invariant Metric
Thermodynamics
Specific Heat
Specific heat
transition points
thermodynamics
Curvature
Black Hole Thermodynamics
Singularity
curvature
specific heat
Statistical mechanics
Angular momentum
Invariance
Angular Momentum

Keywords

  • statistical mechanics
  • phase transitions
  • black hole thermodynamics
  • information geometric methods

Cite this

Geometrothermodynamics of the Kehagias–Sfetsos black hole. / Janke, W.; Johnston, D.A.; Kenna, Ralph.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 42, 2010, p. 425206.

Research output: Contribution to journalArticle

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