Abstract
Using Maxwell’s equal area law, we discuss the phase transition of higher dimensional charged topological dilaton AdS black hole with a nonlinear source. The coexisting region of the two phases is found and we depict the coexistence region in the P–v diagrams. The two-phase equilibrium curves in the P–T diagrams are plotted, and we take the first order approximation of volume v in the calculation. To better compare with a general thermodynamic system, the Clapeyron equation is derived for a higher dimensional charged topological black hole with a nonlinear source. The latent heat of an isothermal phase transition is investigated. We also study the effect of the parameters of the black hole on the region of two-phase coexistence. The results show that the black hole may go through a small–large phase transition similar to those of usual non-gravity thermodynamic systems.
Highlights
Black holes have been used as the laboratory of many kinds of theories, specially the thermodynamics of the black hole plays an important role
The isotherms in P–v diagrams of charged topological dilaton AdS black holes in Ref. [15] show that there exists a thermodynamically unstable region with ∂ P/∂v > 0 when the temperature is below the critical temperature and the negative pressure emerges when temperature is below a certain value
We extend the Maxwell equal area law to n-dimensional charged topological dilaton AdS black hole to establish a phase transition process of the black hole as a thermodynamic system
Summary
It may seem a little surprising that one elevate to the status of a thermodynamic variable. is usually thought of as an energy in the Einstein action. It has been thought that the statistical-mechanical calculation of the Bekenstein–Hawking entropy for a class of supersymmetric black holes in five dimensions is one of the remarkable results in string theory [62,63] Another motivation for studying higher dimensional black holes originates from the braneworld scenarios, as a new fundamental scale of quantum gravity. In this paper, using the Maxwell’s equal area law, we establish a phase transition process in charged topological dilaton AdS black holes, where the issues about unstable states and negative pressure are resolved. Outline of this paper is as follows: the higher dimensional charged topological dilaton AdS black hole as a thermodynamic system is briefly introduced in Sect. 3, by the Maxwell equal area law the phase transition processes at certain temperatures are obtained and the boundary of twophase equilibrium region are depicted in the P–v diagram for a higher dimensional charged topological dilaton AdS black hole.
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