### Abstract

Original language | English |
---|---|

Pages (from-to) | 425206 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 43 |

Issue number | 42 |

DOIs | |

Publication status | Published - 2010 |

### Fingerprint

### Keywords

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

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*43*(42), 425206. https://doi.org/10.1088/1751-8113/43/42/425206

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

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 43, no. 42, pp. 425206. https://doi.org/10.1088/1751-8113/43/42/425206

}

TY - JOUR

T1 - Geometrothermodynamics of the Kehagias–Sfetsos black hole

AU - Janke, W.

AU - Johnston, D.A.

AU - Kenna, Ralph

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - statistical mechanics

KW - phase transitions

KW - black hole thermodynamics

KW - information geometric methods

U2 - 10.1088/1751-8113/43/42/425206

DO - 10.1088/1751-8113/43/42/425206

M3 - Article

VL - 43

SP - 425206

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 42

ER -