Thermodynamics of $d$-Dimensional Charged AdS (Anti-de Sitter) Black Holes: Hamiltonian Approach and Clapeyron Equation

Abstract

The study of thermodynamics in the view of the Hamiltonian approach is a newest tool to analyze the thermodynamic properties of the black holes. In this letter, we investigate the thermodynamics of $d$-dimensional ($d>3$) asymptotically AntideSitter black holes. A thermodynamic representation based on symplectic geometry is introduced in this letter. We extend the thermodynamics of $d-$dimensional charged AntideSitter black holes in the views of a Hamiltonian approach. Firstly, we study the thermodynamics in reduced phase space and correlate with the Schwarzschild solution. Then we enhance it in the extended phase space. In an extended phase space the thermodynamic equations of state are stated as constraints. We apply the canonical transformation to analyze the thermodynamics of said type of black holes. We plot $P$-$v$ diagrams for different dimensions $d$ taking the temperatures $T<T_c,T=T_c$ and $T>T_c$ and analyze the natures of the graphs and the dependencies on $d$. In theses diagrams, we point out the regions of coexistence. We also examine the phase transition by applying "Maxwell's equal area law" of the said black holes. Here we find the regions of coexistence of two phases which are also depicted graphically. Finally, we derive the "Clapeyron equation" and investigate the latent heat of isothermal phase transition.

16 pages, 9 figures

References in corpus (9)

• Thermodynamics of de Sitter Black Holes: Thermal Cosmological Constant
• Mechanical First Law of Black Hole Spacetimes with Cosmological Constant and Its Application to Schwarzschild-de Sitter Spacetime
• Spherically symmetric brane spacetime with bulk $f(\mathcal{R})$ gravity
• A Hamilton-Jacobi Formalism for Thermodynamics
• Phase transitions for the topological de Sitter spaces and Schwarzschild-de Sitter black hole
• Thermodynamic Variables of First-Order Entropy Corrected Lovelock-AdS Black Holes : P-V Criticality Analysis
• Thermodynamic Studies of Different Black Holes with Modifications of Entropy
• Nature of singularity formed by the gravitational collapse in Husain space-time with electromagnetic field and scalar field
• A Study of Phase Transition in Black Hole Thermodynamics

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