Thermodynamic volume and the extended Smarr relation

Seungjoon Hyun, Jaehoon Jeong, Sang A. Park, Sang Heon Yi

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


We continue to explore the scaling transformation in the reduced action formalism of gravity models. As an extension of our construction, we consider the extended forms of the Smarr relation for various black holes, adopting the cosmological constant as the bulk pressure as in some literatures on black holes. Firstly, by using the quasi-local formalism for charges, we show that, in a general theory of gravity, the volume in the black hole thermodynamics could be defined as the thermodynamic conjugate variable to the bulk pressure in such a way that the first law can be extended consistently. This, so called, thermodynamic volume can be expressed explicitly in terms of the metric and field variables. Then, by using the scaling transformation allowed in the reduced action formulation, we obtain the extended Smarr relation involving the bulk pressure and the thermodynamic volume. In our approach, we do not resort to Euler’s homogeneous scaling of charges while incorporating the would-be hairy contribution without any difficulty.

Original languageEnglish
Article number48
JournalJournal of High Energy Physics
Issue number4
Publication statusPublished - 2017 Apr 1

Bibliographical note

Publisher Copyright:
© 2017, The Author(s).

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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