Nonlinearly charged black hole chemistry with massive gravitons in the grand canonical ensemble

2020/10/31 by Ali Dehghani, S. H. Hendi, Seyed Hossein Hendi
Physics and Astronomy · #AdS black hole #Black Holes and Theoretical Physics #Black hole (networking) #Canonical ensemble #Cosmology and Gravitation Theories #Critical phenomena #Grand canonical ensemble #Gravitation #Graviton #Invariant (physics) #Massive gravity #Mathematical physics #Microcanonical ensemble #Phase transition #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Theoretical physics #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.104.024025

published as Phys. Rev. D 104, 024025 (2021) · 21 pages, 4 figures, 2 tables - Published version

openalex publication_date 2021/07/13 · arxiv created 2021/09/17 · arxiv updated 2021/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In the context of black hole chemistry (BHC), holographic phase transitions of asymptotically anti--de Sitter (AdS) charged topological black holes (TBHs) in massive gravity coupled to power Maxwell invariant (PMI) electrodynamics are discussed in the grand canonical (fixed U(1) potential, \mathrm\ensuremathΦ) ensemble. Considering the higher-order of graviton's self-interactions of (dRGT) massive gravitational field theory in arbitrary dimensions, we derive exact TBH solutions. We also calculate the explicit form of the on-shell action and the associated thermodynamic quantities in the grand canonical ensemble (GCE). Besides, we examine the validity of the first law of thermodynamics and Smarr relation in the extended phase space thermodynamics. Regarding this model, we show that (a) a van der Waals (vdW) behavior takes place in d\ensuremath≥4 dimensions, (b) a typical reentrant phase transition can happen in d\ensuremath≥5, and (c) both anomalous vdW and triple point phenomena are recognized in d\ensuremath≥6. Accordingly, we find that the obtained results are quite different from their counterparts in the GCE of Maxwell-massive gravity. Furthermore, we briefly study the critical behaviors of higher-dimensional TBHs with a conformally invariant Maxwell source as a specific subclass of our solutions for Einstein's theory and the massive gravity in various ensembles.

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