Hawking-Page Phase Transition Research Articles

Thermodynamics of the Einstein-Maxwell system

At first glance, thermodynamic properties of gravity with asymptotically AdS conditions and those with box boundary conditions, where the spatial section of the boundary is a sphere of finite radius, appear similar. Both exhibit a similar phase structure and Hawking-Page phase transition. However, when we introduce a U(1) gauge field to the system, discrepancies in thermodynamic properties between the two cases has been reported in [7] (JHEP 11 (2016) 041). In this paper, by accepting the assumption that all Euclidean saddles contribute to the partition function, I found that these discrepancies are resolved due to the contribution from the “bag of gold (BG),” which is the class of Euclidean geometries whose area of bolt is bigger than that of the boundary. As a result, the Hawking-Page phase structure is restored, with the unexpected properties that the upper bound of thermodynamic entropy is always larger than the boundary area divided by 4G when the chemical potential is non-zero, and that such high entropy states are realized at sufficiently high temperature.

Rényi topology of charged-flat black hole: Hawking-Page and Van-der-Waals phase transitions

In this paper, we extend the proposed setup in Wei et al. (2022); Yerra et al. (2022) for finding the topological charges associated with the Hawking-Page and Van-der-Waals transition points as well as equilibrium phases to catch the nonextensive nature of the black hole entropy. Rigorously speaking we incorporate the Rényi statistics formalism in off-shell Bragg-Williams free energy landscape, to examine topologically the Hawking-Page phase transition related to the uncharged/charged asymptotically flat black hole in grand canonical and the Van-der-Waals transition in the canonical ensemble, where a vortex/anti-vortex structure is found. For this purpose, we introduce three mappings, the ψ- and ξ-mapping, for phase transitions classification and the η-mapping for equilibrium phases classification. We found that Hawking-Page and Van-der-Waals phase transitions belong to different topological classes and exhibit an interplay of total charge values hinting to a possible new correspondence.Our topological study provides further substantiation for a possible conjecture positing a correspondence between the thermodynamic characteristics of black holes in asymptotically flat spacetime using Rényi statistics, and those in asymptotically Anti-de-Sitter spacetime employing Gibbs-Boltzmann statistics.

Local Poincaré algebra from quantum chaos

The local two-dimensional Poincaré algebra near the horizon of an eternal AdS black hole, or in proximity to any bifurcate Killing horizon, is generated by the Killing flow and outward null translations on the horizon. In holography, this local Poincaré algebra is reflected as a pair of unitary flows in the boundary Hilbert space whose generators under modular flow grow and decay exponentially with a maximal Lyapunov exponent. This is a universal feature of many geometric vacua of quantum gravity. To explain this universality, we show that a two-dimensional Poincaré algebra emerges in any quantum system that has von Neumann subalgebras associated with half-infinite modular time intervals (modular future and past subalgebras) in a limit analogous to the near-horizon limit. In ergodic theory, quantum dynamical systems with future or past algebras are called quantum K-systems. The surprising statement is that modular K-systems are always maximally chaotic.Interacting quantum systems in the thermodynamic limit and large N theories above the Hawking-Page phase transition are examples of physical theories with future/past subalgebras. We prove that the existence of (modular) future/past von Neumann subalgebras also implies a second law of (modular) thermodynamics and the exponential decay of (modular) correlators. We generalize our results from the modular flow to any dynamical flow with a positive generator and interpret the positivity condition as quantum detailed balance.

Thermodynamics of deformed AdS-Schwarzschild black hole

By implementing the gravitational decoupling method, we find the deformed AdS-Schwarzschild black hole solution when there is also an additional gravitational source, which obeys the weak energy condition. We also deliberately choose its energy density to be a certain monotonic function consistent with the constraints. In the method, there is a positive parameter that can adjust the strength of the effects of the geometric deformations on the background geometry, which we refer to as a deformation parameter. The condition of having an event horizon limits the value of the deformation parameter to an upper bound. After deriving various thermodynamic quantities as a function of the event horizon radius, we mostly focus on the effects of the deformation parameter on the horizon structure, the thermodynamics of the solution and the temperature of the Hawking–Page phase transition. The results show that with the increase of the deformation parameter: the minimum horizon radius required for a black hole to have local thermodynamic equilibrium and the minimum temperature below which there is no black hole decrease, and the horizon radius of the phase transition and the temperature of the first-order Hawking–Page phase transition increase. Furthermore, when the deformation parameter vanishes, the obtained thermodynamic behavior of the black hole is consistent with that stated in the literature.

Thermodynamical phase transitions of AdS black hole in Horava–Lifshitz gravity

In this paper, we investigate the thermodynamical phase transitions of the spherically symmetric AdS black hole in Horava–Lifshitz (HL) gravity for the detailed balance violation parameter [Formula: see text]. First, by calculating the HP temperature [Formula: see text], the minimum temperature [Formula: see text] and the Gibbs free energy [Formula: see text] of the AdS black hole in different values of parameter [Formula: see text], we find that the HP phase transition can occur at all pressures. Comparing the HP temperature [Formula: see text] with the minimum temperature [Formula: see text], we notice that the ratio of [Formula: see text] tends to 1 when [Formula: see text]. Second, for the small–large black hole phase transition of the AdS black hole, we discover that the black hole heat capacity is divergent at the minimum temperature [Formula: see text], the small–large black hole phase transition occurs at the same time. Furthermore, the black hole entropy also exists [Formula: see text] when [Formula: see text], and [Formula: see text] when the black hole temperature has its minimum [Formula: see text], we surprisingly find that the ratio of [Formula: see text] tends to [Formula: see text] when the dimension [Formula: see text], which provides a general relation between the Hawking–Page phase transition and the small–large black hole phase transition of the AdS black hole in the large dimension. All in all, the ratios of typical temperature and entropy of two kinds of phase transitions tend to natural constant in the large dimension limit, which may imply to understand the nature of two different phase transitions.

State dependence of Krylov complexity in 2d CFTs

We compute the Krylov Complexity of a light operator O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}L in an eigenstate of a 2d CFT at large central charge c. The eigenstate corresponds to a primary operator O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}H under the state-operator correspondence. We observe that the behaviour of K-complexity is different (either bounded or exponential) depending on whether the scaling dimension of O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}H is below or above the critical dimension hH = c/24, marked by the 1st order Hawking-Page phase transition point in the dual AdS3 geometry. Based on this feature, we hypothesize that the notions of operator growth and K-complexity for primary operators in 2d CFTs are closely related to the underlying entanglement structure of the state in which they are computed, thereby demonstrating explicitly their state-dependent nature. To provide further evidence for our hypothesis, we perform an analogous computation of K-complexity in a model of free massless scalar field theory in 2d, and in the integrable 2d Ising CFT, where there is no such transition in the spectrum of states.

Information loss, mixing and emergent type III1 factors

A manifestation of the black hole information loss problem is that the two-point function of probe operators in a large Anti-de Sitter black hole decays in time, whereas, on the boundary CFT, it is expected to be an almost periodic function of time. We point out that the decay of the two-point function (clustering in time) holds important clues to the nature of observable algebras, states, and dynamics in quantum gravity.We call operators that cluster in time “mixing” and explore the necessary and sufficient conditions for mixing. The information loss problem is a special case of the statement that in type I algebras, there exists no mixing operators. We prove that, in a thermofield double state (KMS state), if mixing operators form an algebra (close under multiplication), the resulting algebra must be a von Neumann type III1 factor. In other words, the physically intuitive requirement that all nonconserved operators should exponentially mix is so strong that it fixes the observable algebra to be an exotic algebra called a type III1 factor. More generally, for an arbitrary out-of-equilibrium state of a general quantum system (von Neumann algebra), we show that if the set of operators that mix under modular flow forms an algebra, it is a type III1 von Neumann factor.In a theory of Generalized Free Fields (GFF), we show that if the two-point function clusters in time, all operators are mixing, and the algebra is a type III1 factor. For example, in \U0001d4a9 = 4 SYM, above the Hawking-Page phase transition, clustering of the single trace operators implies that the algebra is a type III1 factor, settling a recent conjecture of Leutheusser and Liu. We explicitly construct the C∗-algebra and von Neumann subalgebras of GFF associated with time bands and, more generally, open sets of the bulk spacetime using the HKLL reconstruction map.

Thermodynamics and phase transition structure of charged black holes in f(R) gravity background from Rényi statistics perception

In the current study, we investigate the Rényi statistics as an extension of the Boltzmann-Gibbs theory, in order to characterize the non-Boltzmannian phase structure of charged black holes in the f(R) gravity. Through this research, we discover that a Hawking-Page phase transition and a Van-der-Waals phase portrait, which are missing from the standard Boltzmann-Gibbs' description, emerge respectively within the grand canonical ensemble and canonical ensemble via the Rényi formalism.The thermodynamics associated with charged black holes without cosmological constant black holes using Rényi statistics processes the same properties as those of asymptotically AdS charged black holes via Gibbs-Boltzmann formalism, as further evidenced by such phase structures found here. This is another example of a potential and substantial relationship between the cosmological constant and the nonextensive Rényi parameter.

4D-EGB black holes in RPS thermodynamics

In this paper, we study thermodynamics of charged and uncharged 4-Dimension Einstein-Gauss–Bonnet (4D-EGB) black holes. The context of this study is the Visser’s holographic thermodynamics with a fixed anti-de Sitter radius and a variable Newton constant known as restricted phase space thermodynamics (RPST). Our setup is constructed by using the AdS/CFT correspondence and by introducing a conjugate quantity of the Gauss–Bonnet parameter. By this ansatz, we conclude that the Gauss–Bonnet action multiplied by a temperature, behaves as a free energy. We derive the conjugate quantities corresponding to the first law in the RPST formalism. The study of the T−S processes and the effect of the Gauss–Bonnet constant, α, show that thermodynamic properties of charged black holes depend on the Gauss–Bonnet term and the charge of black holes. For an uncharged black holes, the effect of Gauss–Bonnet becomes crucial, as it behaves as a charged black hole with an effective charge. Finally, we find that the Hawking-Page phase transition occurs between a large black hole and a thermal AdS space.

Thermodynamics and phase transition of Bardeen black hole via Rényi statistics in grand canonical ensemble and canonical ensemble

The thermodynamics of the Bardeen black hole in asymptotically flat space is investigated with the corrected first law of thermodynamics via Rényi statistics. The nonextensive parameter lambda gives the possibility to the thermal stability of Bardeen black hole, and there is a Hawking–Page phase transition in the grand canonical ensemble (fixed the potential), which is similar to the cases of Bardeen black hole and corrected Bardeen black hole in asymptotically anti-de Sitter (AdS) space via standard Gibbs–Boltzmann (GB) statistics. By introducing the general Smarr formula via Rényi statistics, the thermodynamic pressure P is defined with the parameter lambda and its conjugate quantity V is the thermodynamic volume (not a geometric spherical volume with horizon radius r_{h}). The thermodynamics of the asymptotically flat Bardeen black hole via Rényi statistics in the canonical ensemble (fixed the charge q) behaves like the van der Waals system, which is also same as the asymptotically Bardeen-AdS black hole via GB statistics. The analogy between the thermodynamics of the asymptotically flat Bardeen black hole from Rényi statistics and the Bardeen-AdS black hole from GB statistics makes us to consider what is the relation between the nonextensive parameter lambda and the cosmological constant Lambda .

Bulk-boundary thermodynamic equivalence: a topology viewpoint

Setting the cosmological constant to be dynamical, we study the bulk and boundary thermodynamics of charged Anti-de Sitter black holes. We develop mass/energy formulas in terms of thermodynamic state functions for the extended thermodynamics, mixed thermodynamics, and boundary conformal field theory thermodynamics. We employ the residue method to study the topological properties of the phase transitions. Our analysis reveals that the bulk and boundary thermodynamics are topologically equivalent for both criticalities and first-order phase transitions in the canonical ensembles, as well as for the Hawking-Page(-like) phase transitions in the grand canonical ensembles. Additionally, those three kinds of phase transitions are shown to be distinguished by their unique topological charges. Our results exemplify the gravity-gauge duality in terms of topology.

Subregion entropy for the doubly-holographic global black string

We study the growth of entanglement entropy in a doubly holographic model of gravity for a spherical AdS black hole. Compared to previous work, which was limited to the case of planar black holes, this introduces an extra scale to the problem. This allows us to analyze the interplay between the reorganization of entanglement entropy due to island formation and the onset of the Hawking-Page phase transition and to find the appearance of a new critical black hole radius unrelated to the thermodynamics. We also find that the geometry of the Ryu-Takayanagi surface capturing the physics of islands exhibits drastically different behavior than in the planar case.

Page curve and phase transition in deformed Jackiw–Teitelboim gravity

We consider the entanglement island in a deformed Jackiw–Teitelboim black hole in the presence of the phase transition. This black hole has the van der Waals–Maxwell-like phase structure as it is coupled with a Maxwell field. We study the behavior of the Page curve of this black hole by using the island paradigm. In the fixed charge ensemble, we discuss different situations with different charges that influence the system’s phase structure. There is only a Hawking–Page phase transition in the absence of charges, which leads to an unstable small black hole. Hence, the related Page curve does not exist. However, a van der Waals–Maxwell-like phase transition occurs in the presence of charges. This yields three black hole solutions. The Page curve of the middle size black hole does not exist. For the extremal black hole, the Page time approaches zero in the phase transition situation but becomes divergent without the phase transition. In a word, we study the Page curve and the island paradigm for different black hole phases and in different phase transition situations.

Impact of exponential entropy on the thermodynamics of 4D charged Einstein-Guass-Bonnet-AdS black hole

In the presence of exponential corrected entropy, we investigate the thermal stability and phase transitions of a charged 4D Einstein-Gauss-Bonnet-AdS black hole by using the formalism known as the deflection angle formalism. Specifically, with the help of the elliptic function analysis, we investigate the phase structure of the black hole by focusing on the optical aspects. This has come to our attention that the thermal variation of the deflection angle can be used to generate both stable and unstable phases. The Hawking-Page phase transition, which is derived from the Gibbs free energy optical dependence, is another issue that we investigate with the help of exponentially corrected entropy. In addition, there are particular points along the deflection angle that produce a transition between large and small black holes. Our Gibbs free energy versus deflection angle behavior showed that the deflection angle can be utilized as a relevant quantity to determine the critical behavior of AdS black holes. In the presence of exponential corrected entropy, the thermodynamic geometry of a charged 4D Einstein-Guass-Bonnet-AdS black hole is also discussed.

Thermodynamic Phase Transition of Generalized Ayon-Beato Garcia Black Holes

In this work, we study thermodynamics of generalized Ayon-Beato and Garcia (ABG) black hole metric which contains three parameters named as mass m , magnetic charge q , and dimensionless coupling constant of nonlinear electrodynamics interacting field γ . We showed that central regions of this black hole behaves as dS (AdS) vacuum space by setting q < 2 m q > 2 m and in the case q = 2 m reaches to a flat Minkowski space. In the large distances, this black hole behaves as a Reissner-Nordstrom BH. However, an important role of the charge q appeared in the production of a formal variable cosmological parameter which will support pressure coordinate in the thermodynamic perspective of this black hole in our setup. We should point that this formal variable cosmological parameter is different with cosmological constant which comes from AdS/CFT correspondence, and it is effective at large distances as AdS space pressure. In our setup, the assumed pressure originated from the internal material of the black hole say q and m here. By calculating the Hawking temperature of this black hole, we obtain equation of state. Then, we plotted isothermal P-V curves and heat capacity at constant pressure. They show that the system participates in the small to large phase transition of the black hole or the Hawking-Page phase transition which is similar to the van der Waals phase transition in the ordinary thermodynamics systems. In fact in the Hawking-Page phase transition disequilibrium, evaporating generalized ABG black hole reaches to a vacuum AdS space finally.

A black hole solution in conformal supergravity

We present a three-parameter family of analytic black-hole solutions in the bosonic sector of a four-dimensional supersymmetric model with matter fields in the adjoint representation. The solutions are endowed with a curvature and torsional singularities which are both surrounded by an event horizon. They are asymptotically Lorentz flat, representing the torsional generalization of the Riegert black hole in conformal gravity. We compute the partition function to first order in the saddle-point approximation which turns out to be finite without any reference to boundary counterterms. We find a non-maximmally symmetric thermalized ground state, whose existence is relevant when studying Hawking-Page phase transitions. Finally, we discuss future directions regarding its extended phase space.

Thermodynamics of asymptotically de Sitter black hole in dRGT massive gravity from Rényi entropy

The thermodynamic properties of the de Rham–Gabadadze–Tolley (dRGT) black hole in the asymptotically de Sitter (dS) spacetime are investigated by using Rényi entropy. It has been found that the black hole with asymptotically dS spacetime described by the standard Gibbs–Boltzmann statistics cannot be thermodynamically stable. Moreover, there generically exist two horizons corresponding to two thermodynamic systems with different temperatures, leading to a nonequilibrium state. Therefore, in order to obtain the stable dRGT black hole, we use the alternative Rényi statistics to analyze the thermodynamic properties in both the separated system approach and the effective system approach. Interestingly, we found that it is possible concurrently obtain positive pressure and volume for the dRGT black hole while it is not for the Schwarzschild-de Sitter (Sch-dS) black hole. Furthermore, the bounds on the nonextensive parameter for which the black hole being thermodynamically stable are determined. In addition, the key differences between the systems described by different approaches, e.g., temperature profiles and types of the Hawking–Page phase transition are pointed out.

High dimensional AdS-like black hole and phase transition in Einstein-bumblebee gravity* *Supported by the Scientific Research Fund of the Hunan Provincial Education Department (19A257 and 19A260), the National Natural Science Foundation (NNSFC) of China (11247013), Hunan Provincial Natural Science Foundation of China (2015JJ2085)

In this study, we obtained an exact high dimensional anti-de Sitter (AdS) black hole solution in Einstein-bumblebee gravity theory. This AdS-like black hole can only exist with a linear functional potential of the bumblebee field. We found that the Smarr formula and the first law of black hole thermodynamics can still be constructed in this Lorentz symmetry breaking black hole spacetime, but the conceptions of the black hole horizon area/entropy and the volume inside the horizon should be renewed due to its anisotropy. We also found that two types of phase transition exist: small-large black hole phase transition and Hawking-Page phase transition, like those of the Schwarzschild AdS black hole. After Lorentz symmetry breaking, the black hole mass at the divergent point of heat capacity becomes small, and the Gibbs free energy of the meta-stable large black hole is also smaller, showing that the large stable black hole can be more easily formed.

Black hole thermodynamics in asymptotically safe gravity

We have investigated the black hole thermodynamics and the phase transition for renormalized group improved asymptotically safe Schwarzschild black hole. This geometry takes into account the quantum gravitational correction in the running gravitational constant identifying \(G(r) \equiv G(k=k(r))\). We studied various thermodynamic quantity like the Hawking temperature, specific heat and entropy for the general parameter \(\gamma \) for quantum corrected Schwarzschild metric. We have noticed that the coefficient of the leading quantum correction, that is, the logarithmic correction gets affected by the presence of \(\gamma \). We further study the local temperature, thermal stability of the black hole and the free energy considering a cavity enclosing the black hole. According to the local specific heat, there exists three black hole states, among them the large and tiny black hole are thermally stable states. We further investigate the on-shell free energy and find that no Hawking-Page phase transition occurs here unlike the ordinary Schwarzschild black hole. The black hole state always prevails for all temperatures. Also, we have found two critical points, \(T_{c1}\) and \(T_{c2}\), corresponding to the phase transition from one black hole state to another.

Non-Markovian dynamics of black hole phase transition

We provide a comprehensive study on the non-Markovian dynamics of the black hole phase transitions based on the underlying free energy landscape. By assuming that the transition processes between different black hole states are stochastic, the non-Markovian dynamics of the black hole phase transition is governed by the generalized Langevin equation with the time-dependent friction that represents the memory effect from the effective thermal bath when the timescale of the system is comparable or shorter than the timescale of the effective thermal bath. We consider the first passage problem associated with the black hole phase transitions and derive the analytical expressions of the mean first passage time in the weak, intermediate, and large friction regimes. As the concrete examples, we study the effects of three types of time dependent friction kernel (delta function friction, exponentially decayed friction, and oscillatory friction) on the dynamics of Hawking-Page phase transition and the small/large RNAdS black hole phase transition. we found that there is a kinetic turnover point for each type of friction kernel when the friction strength varies. For the exponentially decayed friction kernel, it is shown that the non-Markovian effect slows down the phase transition dynamics in the weak friction regime and speeds up the transition process in the strong friction regime. For the oscillating decayed friction kernel, we found kinetic resonances when the oscillating frequency of the effective thermal bath is equal to the oscillating frequency of the black hole state in the initial potential well on the free energy landscape.