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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

It is known Lorentz symmetry which is one of most important symmetries in nature; however, some researches indicate that the Lorentz symmetry might be violated in the ultraviolet limit [

Recently, Schwarzschild black holes, Schwarzschild AdS black holes, and Reissner-Nordstrom black holes in rainbow gravity [

The paper is organized as follows. In the next section, by using the HUP and the modified dispersion relation, we obtain deformed temperature, and we also calculate heat capacity with a fixed charge and discuss the thermal stability. In Section

In rainbow gravity the line element of the modified charged AdS black holes can be described as [

In gravity’s rainbow, although the metric depends on the energy of test particle, the usual HUP can be still used [

Generally, the standard temperature was given by [

In general, the thermal stability can be determined by the heat capacity, which is also used to the systems of black holes [

The heat capacity with a fixed charge can be calculated as

The numerical methods indicate there are three situations corresponding to zero, one, and two diverging points of heat capacity respectively, which have been described in Figures

Surprisingly, although rainbow functions modify the

Since David Kubiznak and Robert B. Mann have showed the critical behaviour of charged AdS black holes and completed the analogy of this system with the liquid-gas system [

Based on [

Gibbs free energy of charged AdS black holes in rainbow gravity. The blue line

In this paper, we have studied the thermodynamic behavior of charged AdS black holes in rainbow gravity. By the modified dispersion relation and HUP, we got deformed temperature in charged AdS black holes using no-zero mass of test particle. We have discussed the divergence about the heat capacity with a fixed charge. Our result shows that the phase structure has a relationship with AdS radius

We find the mass of test particle does not influence the forms of temperature, entropy, and heat capacity but only changes their amplitudes. Moreover, there is a special value about the mass of test particle encountered

No data were used to support this study.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

We would like to thank the National Natural Science Foundation of China (Grant no. 11571342) for supporting us on this work.