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Thermodynamical stability of f(R)-AdS black holes in grand canonical ensemble

  • Ming Zhang
Research Article

Abstract

In this paper, n-dimensional (\(n=4p, p\) is a positive integer) f(R)-AdS black holes is divided into Schwazschild-AdS (SAdS) like ones and Reissner–Nordström-AdS (RN-AdS) like ones. Thermodynamical stability of them in grand canonical ensemble is investigated. Locally, we find that the RN-AdS like f(R) black holes will experience either type-one or type-two phase transitions from unstable states to stable states, whereas there are only type-two phase transitions between that two states for SAdS like f(R) black holes. Globally, we find that there are type-one Hawking–Page like phase transitions between thermal AdS state and f(R) black holes. Using thermodynamical geometry method, we find that thermodynamical extrinsic curvature can only provide accurate stability information near type-two (not type-one) phase transition points for f(R) black holes in grand canonical ensemble.

Keywords

Thermodynamical stability f(R) black hole Grand canonical ensemble 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11235003).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Physics, Institute of Theoretical PhysicsBeijing Normal UniversityBeijingChina

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