Black Hole Chemistry Research Articles

Topology of nonlinearly charged black hole chemistry via massive gravity

The classification of critical points of charged topological black holes (TBHs) in anti-de Sitter spacetime (AdS) under the Power Maxwell Invariant (PMI)-massive gravity is accomplished within the framework of black hole chemistry (BHC). Considering the grand canonical ensemble (GCE), we show that d=4 black hole have only one topological class, whereas dge 5 black holes belong to two different topology classes. Furthermore, the conventional critical point characterized by negative topological charge coincides with the maximum extreme point of temperature; and the novel critical point featuring opposite topological charge corresponds to the minimum extreme point of temperature. With increasing pressure, new phases emerge at the novel critical point while disappear from the conventional one. Moreover, a atypical van der Waals (vdW) behavior is found in dge 6 dimensions, and the anomaly disappears at the traditional critical point. In the limit of nonlinearity parameter srightarrow 1, different topology classes are only obtained in the GCE and they may not exist within the canonical ensemble. With the absence of electric potential Phi , the neutral TBHs share the same topological classification results as the charged TBHs in the GCE of Maxwell-massive gravity.

Statistical ensembles and logarithmic corrections to black hole entropy

In this paper, we consider general statistical ensembles and compute logarithmic corrections to the microcanonical entropy resulting due to thermodynamic fluctuations which are controlled by the boundary conditions, i.e. due to choice of ensemble. The framework is applied to the case of non-extremal black holes to give certain logarithmic corrections to the Bekenstein–Hawking entropy. We argue that within the framework of black hole chemistry, where the cosmological constant is identified with bulk pressure, the isoenthalpic-isobaric entropy rather than microcanonical entropy carries a more natural and consistent thermodynamic interpretation as black hole entropy. Logarithmic corrections to both microcanonical and isoenthalpic-isobaric entropies of black holes are computed, and we show that the latter set of corrections in black hole chemistry are of the same form as corrections to the microcanonical entropy in theories where the cosmological constant is not interpreted as a thermodynamic pressure. Finally, we compute logarithmic corrections to entropy in the framework of holographic black hole chemistry. We emphasize upon the choice of statistical ensemble, both in the bulk and on the boundary, in order to have a consistent comparison between them. The corrections studied in this paper are distinct from those obtained from Euclidean quantum gravity.

Contact and metric structures in black hole chemistry

We review recent studies of contact and thermodynamic geometry for black holes in AdS spacetimes in the extended thermodynamics framework. The cosmological constant gives rise to the notion of pressure P = −Λ/8π and, subsequently a conjugate volume V, thereby leading to a close analogy with hydrostatic thermodynamic systems. To begin with, we review the contact geometry approach to thermodynamics in general and then consider thermodynamic metrics constructed as the Hessians of various thermodynamic potentials. We then study their correspondence to statistical ensembles for systems with two-dimensional spaces of equilibrium states. From the zeroes and divergences of the curvature scalar obtained from the metric, we carefully analyze the issue of ensemble non-equivalence and show certain complimentary behaviors in the description of a thermodynamic system. Following a thorough analysis of the familiar van der Waals system, we turn our attention to black holes in extended phase space. Considering the example of charged AdS black holes, we discuss the generic features of their thermodynamic geometry in detail. The relationship of the thermodynamic curvature(s) with critical points as well as microscopic interactions in black holes is also briefly explored. We finally set up the thermodynamic geometry for finite temperature gauge theories dual to black holes in AdS via holographic correspondence and comment on recent progress.

Black hole chemistry, the cosmological constant and the embedding tensor

We study black-hole thermodynamics in theories that contain dimensionful constants such as the cosmological constant or coupling constants in Wald’s formalism. The most natural way to deal with these constants is to promote them to scalar fields introducing a (d − 1)-form Lagrange multiplier that forces them to be constant on-shell. These (d − 1)-form potentials provide a dual description of them and, in the context of superstring/supergravity theories, a higher-dimensional origin/explanation. In the context of gauged supergravity theories, all these constants can be collected in the embedding tensor. We show in an explicit 4-dimensional example that the embedding tensor can also be understood as a thermodynamical variable that occurs in the Smarr formula in a duality-invariant fashion. This establishes an interesting link between black-hole thermodynamics, gaugings and compactifications in the context of superstring/supergravity theories.

Komar integrals for theories of higher order in the Riemann curvature and black-hole chemistry

We construct Komar-type integrals for theories of gravity of higher order in the Riemann curvature coupled to simple kinds of matter (scalar and vector fields) and we use them to compute Smarr formulae for black-hole solutions in those theories. The equivalence between f (R) and Brans-Dicke theories is used to argue that the dimensionful parameters that appear in scalar potentials must be interpreted as thermodynamical variables (pressures) and we give a general expression for their conjugate potentials (volumes).

Nonlinearly charged black hole chemistry with massive gravitons in the grand canonical ensemble

In the context of Black Hole Chemistry (BHC), holographic phase transitions of asymptotically anti-de Sitter (AdS) charged topological black holes (TBHs) in massive gravity coupled to Power Maxwell Invariant (PMI) electrodynamics are discussed in the grand canonical (fixed $U(1)$ potential, $\Phi$) ensemble. Considering all higher-order graviton's self-interactions of (dRGT) massive gravitational field theory in arbitrary dimensions, exact TBH solutions are derived, the explicit form of the on-shell action is computed, and the associated thermodynamic quantities in the Grand Canonical Ensemble (GCE) are calculated. In addition, the validity of the first law of thermodynamics and Smarr relation are examined in the extended phase space. Regarding this model, it is shown that a van der Waals (vdW) behavior takes place in $d \ge 4$ dimensions, a typical reentrant phase transition is observed in $d \ge 5$, and both anomalous vdW and triple point phenomena are recognized in $d \ge 6$. So, the results are quite different from their counterparts in the GCE of Maxwell-massive gravity. Besides, we briefly study the critical behaviors of higher-dimensional TBHs with a conformally invariant Maxwell source as a special subgroup of our solutions for both Einstein and massive gravity theories in various ensembles.

Effects of Gauss–Bonnet entropy on thermodynamics of Kiselev black hole

In this paper, the thermodynamics of Reissner–Nordström-anti de Sitter black hole surrounded by quintessence is studied and the impact of the Gauss–Bonnet term is measured. The modified entropy, first law of thermodynamics and corresponding Smarr relation are derived due to the combined action of the Gauss–Bonnet term and quintessence fluid. We study the so-called black hole chemistry from the analysis of the corresponding equation-of-state, conjugate potential and the critical points in the extended phase space. To study the phase transitions, we plotted [Formula: see text], [Formula: see text] and [Formula: see text] diagrams and analyzed the conditions for the coexistence of phases.

Topological black hole chemistry in massive gravity with power-Maxwell invariant field

In this paper, asymptotically AdS black hole solutions of massive gravity in the presence of nonlinear electromagnetic field arisen from the power theory of Maxwell invariant are investigated and the associated Euclidean on-shell action is presented. Using the Euclidean on-shell action, the gravitational partition function in the canonical ensemble is computed in arbitrary dimensions and then thermodynamic quantities of topological black holes are obtained. By extending the thermodynamic phase space, i.e., treating negative cosmological constant as thermodynamic pressure, the first law of thermodynamics as well as associated Smarr formula are examined. Next, the equation of state of topological black holes is obtained and it is proven that the critical point equation of these solutions can exhibit black hole phase transitions similar to those of van der Waals, van der Waals like and solid/liquid/gas (related to triple point) phase transitions in usual thermodynamic systems. Especially, the van der Waals phase transition is observed in 4 and higher dimensions, van der Waals type phase transition can be seen in 6 and higher dimensions, and phase transitions associated with triple point, i.e., small/intermediate/large black hole phase transition may happen in 6 and higher dimensions.

Range of novel black hole phase transitions via massive gravity: Triple points and N -fold reentrant phase transitions

Massive gravities in anti-de Sitter spacetime can be viewed as effective dual field theories of different phases of condensed matter systems with broken translational symmetry such as solids, (perfect) fluids, and liquid crystals. Motivated by this fact, we explore the black hole chemistry (BHC) of these theories and find a new range of novel phase transitions close to realistic ones in ordinary physical systems. We find that the equation of state of topological black holes (TBHs) at their inflection point(s) in $d$-dimensional spacetime reduces to a polynomial equation of degree $(d-4)$, which yields up to $n=(d-4)$ critical points. As a result, for (neutral) TBHs, we observe triple-point phenomena with the associated first-order phase transitions (in $d \ge 7$), and a new phenomenon we call an $N$-fold reentrant phase transition, in which several ($N$) regions of thermodynamic phase space exhibit distinct reentrant phase transitions, with associated virtual triple points and zeroth-order phase transitions (in $d \ge 8$), as well as Van der Waals transitions (in $d \ge 5$) and reentrant (in $d \ge 6$) behavior. We conclude that BHC in higher-dimensional massive gravity is very likely to offer further new surprises.

Charged black hole chemistry with massive gravitons

In the subject of black hole chemistry, a broad variety of critical phenomena for charged topological black holes (TBHs) with massive gravitons (within the framework of dRGT massive gravity) is discussed in detail. Since critical behavior and the nature of possible phase transition(s) crucially depend on the specific choice of ensemble, and, in order to gain more insight into criticality in the massive gravity framework, we perform our analysis in both canonical (fixed charge, Q) and grand canonical (fixed potential, ) ensembles. It is shown that, for charged TBHs in the grand canonical ensemble, the van der Waals (vdW) phase transition could take place in , the reentrant phase transition (RPT) in and the analogue of triple point in , which are different from the results of the canonical ensemble. In the canonical ensemble, the vdW phase transition is observed in , the vdW type phase transition in and the critical behavior associated with the triple point in . In this regard, the appearance of grand canonical criticality and the associated phase transition(s) in black holes with various topologies depend on the effective topological factor instead of k in Einstein’s gravity, where k is the normalized topological factor ( plays this role in the canonical ensemble of TBHs in massive gravity). Such evidence gives the (grand) canonical study of extended phase space thermodynamics with massive gravitons a special significance.

Black hole chemistry and holography in generalized quasi-topological gravity

We investigate the thermodynamics of AdS black holes in Generalized Quasi-topological Gravity with and without electric charge, concentrating on the version of the theory that is cubic in curvature. We study new aspects of Hawking-Page transitions that occur for these black holes. Working within the framework of black hole chemistry, we find a variety of familiar and new critical behaviour and phase transitions in four and higher dimensions for the charged black holes. We also consider some holographic aspects of our work, demonstrating how the ratio of viscosity to entropy is modified by inclusion of these cubic curvature terms.

Reverse Hawking-Page phase transition in de Sitter black holes

In the context of black hole chemistry, we study the thermodynamics of asymptotically de Sitter black holes with conformal scalar hair in Einstein gravity. The hair parameter allows us to attain thermodynamic equilibrium between the event horizon and the cosmological horizon. We find that the system of the black hole and the de Sitter space surrounding it undergo a “Reverse” Hawking-Page phase transition provided we consider the grand-canonical ensemble.

Bardeen black hole chemistry

In the present paper we try to connect the Bardeen black hole with the concept of the recently proposed black hole chemistry. We study thermodynamic properties of the regular black hole with an anti-deSitter background. The negative cosmological constant Λ plays the role of the positive thermodynamic pressure of the system. After studying the thermodynamic variables, we derive the corresponding equation of state and we show that a neutral Bardeen-anti-deSitter black hole has similar phenomenology to the chemical Van der Waals fluid. This is equivalent to saying that the system exhibits criticality and a first order small/large black hole phase transition reminiscent of the liquid/gas coexistence.

BTZ black holes in massive gravity

We analyze certain aspects of BTZ black holes in massive theory of gravity. The black hole solution is obtained by using the Vainshtein and dRGT mechanism, which is asymptotically AdS with an electric charge. We study the Hawking radiation using the tunneling formalism as well as analyze the black hole chemistry for such system. Subsequently, we use the thermodynamic pressure-volume diagram to explore the efficiency of the Carnot heat engine for this system. Some of the important features arising from our solution include the non-existence of quantum effects, critical Van der Walls behaviour, thermal fluctuations and instabilities. Moreover, our solution violates the Reverse Isoperimetric Inequality and, thus, the black hole is super-entropic, perhaps which turns out to be the most interesting characteristics of the BTZ black hole in massive gravity.

Thermodynamics of hairy black holes in Lovelock gravity

We perform a thorough study of the thermodynamic properties of a class of Lovelock black holes with conformal scalar hair arising from coupling of a real scalar field to the dimensionally extended Euler densities. We study the linearized equations of motion of the theory and describe constraints under which the theory is free from ghosts/tachyons. We then consider, within the context of black hole chemistry, the thermodynamics of the hairy black holes in the Gauss-Bonnet and cubic Lovelock theories. We clarify the connection between isolated critical points and thermodynamic singularities, finding a one parameter family of these critical points which occur for well-defined thermodynamic parameters. We also report on a number of novel results, including ‘virtual triple points’ and the first example of a ‘λ-line’ — a line of second order phase transitions — in black hole thermodynamics.

Three-dimensional charged Einstein-aether black holes and the Smarr formula

We investigate the three-dimensional behavior of gravity coupled to a dynamical unit timelike vector: the aether, and present two new classes of exact charged solutions. When c_{13}=0,\Lambda'=0$, we find the solutions is the usual BTZ black hole but now with an universal horizon. In the frame of black hole chemistry, we then calculate the temperature of the universal horizons and, construct the Smarr formulas and first law in the three cases: quasi-asymptotically flat, aether asymptotically flat and quasi-BTZ black hole spacetime. We found these universal horizons obey an exact (or slightly modified) first law of black hole mechanics and may have an entropy and, black hole mass can be interpreted as enthalpy of spacetime. Then the holography may be extended to these horizons under violating Lorentz symmetry.

Lower-dimensional black hole chemistry

The connection between black hole thermodynamics and chemistry is extended to the lower-dimensional regime by considering the rotating and charged BTZ metric in the $(2+1)$-D and a $(1+1)$-D limits of Einstein gravity. The Smarr relation is naturally upheld in both BTZ cases, where those with $Q \ne 0$ violate the Reverse Isoperimetric Inequality and are thus superentropic. The inequality can be maintained, however, with the addition of a new thermodynamic work term associated with the mass renormalization scale. The $D\rightarrow 0$ limit of a generic $D+2$-dimensional Einstein gravity theory is also considered to derive the Smarr and Komar relations, although the opposite sign definitions of the cosmological constant and thermodynamic pressure from the $D>2$ cases must be adopted in order to satisfy the relation. The requirement of positive entropy implies a lower bound on the mass of a $(1+1)$-D black hole. Promoting an associated constant of integration to a thermodynamic variable allows one to define a "rotation" in one spatial dimension. Neither the $D=3$ nor the $D \rightarrow 2$ black holes exhibit any interesting phase behaviour.