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      On the throttling process of the Kerr--Newman--anti-de Sitter black holes in the extended phase space

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          Abstract

          The throttling process of the Kerr--Newman--anti-de Sitter (KN--AdS) black holes is systematically studied in the extended phase space. In this framework, the cosmological constant is interpreted as a varying thermodynamic pressure, and the black hole mass is identified with enthalpy. The throttling process is essentially an isenthalpic (i.e., constant-mass) process for the KN--AdS black holes. The Joule--Thomson coefficient, inversion temperature, inversion curve, and isenthalpic curve are investigated in detail, with both analytical and numerical methods. It is found that there are no maximum inversion temperatures, but only minimum ones that are around one half of the critical temperatures of the KN--AdS black holes.

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          Holography, Thermodynamics and Fluctuations of Charged AdS Black Holes

          , , … (2010)
          The physical properties of Reissner-Nordstrom black holes in (n+1)-dimensional anti-de Sitter spacetime are related, by a holographic map, to the physics of a class of n-dimensional field theories coupled to a background global current. Motivated by that fact, and the recent observations of the striking similarity between the thermodynamic phase structure of these black holes (in the canonical ensemble) and that of the van der Waals-Maxwell liquid-gas system, we explore the physics in more detail. We study fluctuations and stability within the equilibrium thermodynamics, examining the specific heats and electrical permittivity of the holes, and consider the analogue of the Clayperon equation at the phase boundaries. Consequently, we refine the phase diagrams in the canonical and grand canonical ensembles. We study the interesting physics in the neighbourhood of the critical point in the canonical ensemble. There is a second order phase transition found there, and that region is characterized by a Landau-Ginzburg model with A_3 potential. The holographically dual field theories provide the description of the microscopic degrees of freedom which underlie all of the thermodynamics, as can be seen by examining the form of the microscopic fluctuations.
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            Charged AdS Black Holes and Catastrophic Holography

            Andrew Chamblin, Clifford V. Johnson, Robert C. Myers … (1999)
            We compute the properties of a class of charged black holes in anti-de Sitter space-time, in diverse dimensions. These black holes are solutions of consistent Einstein-Maxwell truncations of gauged supergravities, which are shown to arise from the inclusion of rotation in the transverse space. We uncover rich thermodynamic phase structures for these systems, which display classic critical phenomena, including structures isomorphic to the van der Waals-Maxwell liquid-gas system. In that case, the phases are controlled by the universal `cusp' and `swallowtail' shapes familiar from catastrophe theory. All of the thermodynamics is consistent with field theory interpretations via holography, where the dual field theories can sometimes be found on the world volumes of coincident rotating branes.
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              Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume

              D. Kubiznak, M. Cvetic, C. Pope … (2010)
              In a theory where the cosmological constant \(\Lambda\) or the gauge coupling constant \(g\) arises as the vacuum expectation value, its variation should be included in the first law of thermodynamics for black holes. This becomes \(dE= TdS + \Omega_i dJ_i + \Phi_\alpha d Q_\alpha + \Theta d \Lambda\), where \(E\) is now the enthalpy of the spacetime, and \(\Theta\), the thermodynamic conjugate of \(\Lambda\), is proportional to an effective volume \(V = -\frac{16 \pi \Theta}{D-2}\) "inside the event horizon." Here we calculate \(\Theta\) and \(V\) for a wide variety of \(D\)-dimensional charged rotating asymptotically AdS black hole spacetimes, using the first law or the Smarr relation. We compare our expressions with those obtained by implementing a suggestion of Kastor, Ray and Traschen, involving Komar integrals and Killing potentials, which we construct from conformal Killing-Yano tensors. We conjecture that the volume \(V\) and the horizon area \(A\) satisfy the inequality \(R\equiv ((D-1)V/{\cal A}_{D-2})^{1/(D-1)}\, ({\cal A}_{D-2}/A)^{1/(D-2)}\ge1\), where \({\cal A}_{D-2}\) is the volume of the unit \((D-2)\)-sphere, and we show that this is obeyed for a wide variety of black holes, and saturated for Schwarzschild-AdS. Intriguingly, this inequality is the "inverse" of the isoperimetric inequality for a volume \(V\) in Euclidean \((D-1)\) space bounded by a surface of area \(A\), for which \(R\le 1\). Our conjectured {\it Reverse Isoperimetric Inequality} can be interpreted as the statement that the entropy inside a horizon of a given "volume" \(V\) is maximised for Schwarzschild-AdS. The thermodynamic definition of \(V\) requires a cosmological constant (or gauge coupling constant). However, except in 7 dimensions, a smooth limit exists where \(\Lambda\) or \(g\) goes to zero, providing a definition of \(V\) even for asymptotically-flat black holes.
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                Author and article information

                Journal
                Publication date Created: 13 May 2018
                Article
                ArXiV ID: 1805.04861
                SO-VID: 47799b77-fa5c-4c79-98b9-dc073aee9ec0
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Comments 14 pages, 8 figures, comments welcome
                Categories gr-qc

                ScienceOpen disciplines: General relativity & Quantum cosmology
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                ScienceOpen disciplines: General relativity & Quantum cosmology

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