P-V criticality in the extended phase space of black holes in Einstein-Horndeski gravity

Gravity is believed to have a deep and inherent relation to thermodynamics. We study phase transitions and critical behaviors in the extended phase space of asymptotic anti–de Sitter black holes in Einstein-Horndeski gravity. We demonstrate that the black hole in Einstein-Horndeski gravity undergoes a phase transition and P-V criticality mimicking the van der Waals gas-liquid system. The key approach in our study is to introduce a more reasonable pressure instead of the previous pressure P=-Λ/8π related to the cosmological constant Λ, and this proper pressure is motivated by the asymptotical behavior of the black hole. Moreover, we also obtain P-V criticality in the two cases with Λ=0 and Λ>0 for the first time, which implies that the cosmological constant Λ may not be a necessary pressure candidate for black holes at the microscopic level. We present critical exponents for these phase transition processes.

Note:

14 pages, 5 figures, two appendixes and more contents added, version accepted by PRD

General relativity, alternative theories of gravity
black hole: anti-de Sitter
critical phenomena
gravitation: model
phase space
Reissner-Nordstroem
thermodynamics
pressure
gas: van der Waals

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