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.
Highlights
It is known Lorentz symmetry which is one of most important symmetries in nature; some researches indicate that the Lorentz symmetry might be violated in the ultraviolet limit [1,2,3,4,5]
We study the thermodynamical property about the charged AdS black holes in rainbow gravity based on the usual Heisenberg Uncertainty Principle (HUP), p = Δp ∼ 1/r+
Mann have showed the critical behaviour of charged AdS black holes and completed the analogy of this system with the liquid-gas system [22], in what follows we will study whether the critical behavior of the charged AdS black holes system in rainbow
Summary
It is known Lorentz symmetry which is one of most important symmetries in nature; some researches indicate that the Lorentz symmetry might be violated in the ultraviolet limit [1,2,3,4,5]. Based on the deformed energy-momentum dispersion relation the double special relativity has arisen [6, 7]. In this theory, in addition to the velocity of light being the maximum velocity attainable there is another constant for maximum energy scale in nature which is the Planck energy E푃. The rainbow functions f(E/E푃) and g(E/E푃) are required to satisfy lim f In this case, the deformed energy-momentum dispersion relation equation (1) will go back to classical one when the energy of the test particle is much lower than E푝. We study the thermodynamical property about the charged AdS black holes in rainbow gravity based on the usual HUP, p = Δp ∼ 1/r+.
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