Thermodynamic Products in Extended Phase Space

Abstract

We have examined the thermodynamic properties for a variety of spherically symmetric charged-AdS black hole (BH) solutions, including the charged AdS BH surrounded by quintessence dark energy and charged AdS BH in $f(R)$ gravity in \emph{extended phase-space}. This framework involves treating the cosmological constant as thermodynamic variable (for example: thermodynamic pressure and thermodynamic volume). Then they should behave as an analog of Van der Waal (VdW) like systems. In the extended phase space we have calculated the \emph{entropy product} and \emph{thermodynamic volume product} of all horizons. The mass (or enthalpy) independent nature of the said product signals they are \emph{universal} quantities. %Various type of phase diagram of the specific heat has been drawn. The divergence of the specific heat indicates that the second order phase transition occurs under certain condition. In the appendix-A, we have studied the thermodynamic volume products for axisymmetric spacetime and it is shown to be \emph{not universal} in nature. Finally, in appendix-B, we have studied the $P-V$ criticality of Cauchy horizon for charged-AdS BH and found to be an universal relation of critical values between two horizons as $P_c^{-}=P_c^{+}$, $v_c^{-}=v_c^{+}$, $T_c^{-}=-T_c^{+}$, ${\rho }_c^{-}=-{\rho }_c^{+}$. The symbols are defined in the main work.

Accepted in IJMPD

References in corpus (5)

• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Universal Area Product Formulae for Rotating and Charged Black Holes in Four and Higher Dimensions
• Effects of dark energy on P-V criticality of charged AdS black holes
• Inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory
• Thermodynamic Product Formula for Hořava Lifshitz Black Hole

Cited by in corpus (11)

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• Horizon Areas and Logarithmic Correction to the Charged Accelerating Black Hole Entropy
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• $Q-\Phi$ criticality in the extended phase space of $(n+1)$-dimensional RN-AdS black holes
• AdS black holes in the framework of nonlinear electrodynamics, thermodynamics and Joule--Thomson expansion
• Analytic solutions of the geodesic equation for Reissner-Nordström-(anti-)de Sitter black holes surrounded by different kinds of regular and exotic matter fields
• Phase transitions and entropy force of charged de Sitter black holes with cloud of string and quintessence
• General mass formulas for charged Kerr-AdS black holes
• Mass Independent Area (or Entropy) and Thermodynamic Volume Products in Conformal Gravity
• Entropy Product Formula for Gravitational Instanton
• Area products for ${\mathcal{H}}^{\pm }$ in AdS space