# Thermodynamics of Charged AdS Black Holes in Rainbow Gravity

Deng, Jian-Bo  (Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China) ; Li, Ping (Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China) ; He, Miao (Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China) ; Ding, Jia-Cheng (Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China) ; Hu, Xian-Ru  (Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China)

18 December 2018

Abstract: In this paper, the thermodynamic property of charged AdS black holes is studied in rainbow gravity. By the Heisenberg Uncertainty Principle and the modified dispersion relation, we obtain deformed temperature. Moreover, in rainbow gravity we calculate the heat capacity in a fixed charge and discuss the thermal stability. We also obtain a similar behaviour with the liquid-gas system in extending phase space (including $P$ and $r$ ) and study its critical behavior with the pressure given by the cosmological constant and with a fixed black hole charge $Q$ . Furthermore, we study the Gibbs function and find its characteristic swallow tail behavior, which indicates the phase transition. We also find that there is a special value about the mass of test particle which would lead the black hole to zero temperature and a diverging heat capacity with a fixed charge.

Published in: Advances in High Energy Physics 2018 (2018) 1043639