Abstract
In this paper, we have studied the thermodynamic properties of charged AdS black hole with different dimensions under rainbow gravity. At first, by employing the Heisenberg uncertainty principle and the modified dispersion relation and analyzing the effect of rainbow gravity parameter [Formula: see text] and AdS radius [Formula: see text] on the thermodynamics and phase transformation, we have found that the phase structure is related to the AdS radius [Formula: see text] and the heat capacity behaviors are quite similar for different rainbow gravity parameters [Formula: see text] and different dimensions [Formula: see text]. Then, for the rainbow gravity, introducing the analogy between the charged AdS black hole and liquid–gas systems and analyzing the critical behavior of the state equation for charged AdS black hole in different dimensions, the charged AdS black hole has Van der Waals-like phase transitions. At last, we have discussed the relationship between Gibbs free energy [Formula: see text] and Hawking temperature [Formula: see text] in different dimensions and found the typical dovetail behavior, which can be interpreted as a first-order phase transition for the charged AdS black hole under rainbow gravity.
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