AdS Black Holes Research Articles

Nonextensive black hole thermodynamics from generalized Euclidean path integral and Wick’s rotation

This paper extends the Euclidean path integral formalism to account for nonextensive thermodynamics. Concretely, we introduce a generalized Wick’s rotation from real time t to imaginary time τ such that, t→-ifα(τ), where fα a differentiable function and α is a parameter related to nonextensivity. The standard extensive formalism is recovered in the limit α→0 and f0(τ)=τ. Furthermore, we apply this generalized Euclidean path integral to black hole thermodynamics and derive the generalized Wick’s rotations given the nonextensive statistics. The proposed formulation enables the treatment of nonextensive statistics on the same footing as extensive Boltzmann–Gibbs statistics. Moreover, we define a universal measure, η, for the nonextensivity character of statistics. Lastly, based on the present formalism, we strengthen the equivalence between the AdS-Schwarzschild black hole in Boltzmann–Gibbs statistics and the flat-Schwarzschild black hole within Rényi statistics and suggest a potential reformulation of the AdS5/CFT4 duality.

Generalized black hole entropy is von Neumann entropy

It has been argued that, while the individual terms in the generalized entropy, Sgen=A/4GN+Sext, are ill-defined in the semiclassical limit, their sum is well-defined if one takes into account perturbative quantum gravitational effects. The first term diverges as GN→0, and the second diverges due to the infinite entanglement across the horizon which is characteristic of type III von Neumann algebras. It was recently shown that the von Neumann algebra of observables “gravitationally dressed” to the mass of a Schwarzschild-AdS black hole or the energy of an observer in de Sitter spacetime admit a well-defined trace. The algebras are type II∞ (which does not admit a maximum entropy state) and type II1 (which admits a maximum entropy state) respectively, and the von Neumann entropy of “semiclassical” states was found to be (up to an additive constant) the generalized entropy. However, these arguments rely on the existence of a stationary “equilibrium (KMS) state” and do not apply to, for example, black holes formed from gravitational collapse, Kerr black holes, or black holes in asymptotically de Sitter spacetime. These spacetimes are stationary but not in thermal equilibrium. In this paper, we present a general framework for obtaining the algebra of “gravitationally dressed” observables for a linear, Klein-Gordon field on any spacetime with a (bifurcate) Killing horizon. We prove, assuming the existence of a stationary state—which is not necessarily KMS—and suitable asymptotic decay of solutions, a “structure theorem” that the algebra of “gravitationally dressed” observables always contains a type II factor of observables “localized” on the horizon. These assumptions have been rigorously proven in most cases of interest in this paper. Applying our general framework to the algebra of observables in the exterior of an asymptotically flat Kerr black hole where the fields are dressed to the black hole mass and angular momentum we find that the algebra is the product of a type II∞ algebra on the horizon and a type I∞ algebra at past null infinity. The full algebra is type II∞, and the von Neumann entropy of semiclassical states is the generalized entropy. In the case of Schwarzschild-de Sitter, despite the fact that we must introduce an observer, the algebra of observables dressed to the perturbed areas of the black hole and cosmological horizons is the product of type II∞ algebras on each horizon. The entropy of semiclassical states is given by the sum of the areas of the two horizons as well as the entropy of quantum fields in between the horizons. Our results suggest that in all cases where there exists another “boundary structure” (e.g., an asymptotic boundary or another Killing horizon) the algebra of observables is type II∞ and in the absence of such structures (e.g. de Sitter spacetime) the algebra is type II1. Published by the American Physical Society 2025

Thermodynamic aspects of higher-dimensional black holes in Einstein–Gauss–Bonnet gravity through exponential entropy

Abstract We assume exponential corrections to the entropy of $5D$ charged AdS
black hole solutions, which are derived within the framework of
Einstein Gauss-Bonnet gravity and nonlinear electrodynamics.
Additionally, we consider two distinct versions of $5D$ charged AdS
black holes by setting the parameters $q\rightarrow0$ and
$k\rightarrow0$ (where $q$ represents charge, $k$ is the non-linear
parameter). We investigate these black holes in the extended phase
space, where the cosmological constant is interpreted as pressure,
and demonstrate the first law of black hole thermodynamics. The
focus extends to understanding the thermal stability or instability,
as well as identifying first and second-order phase transitions.
This exploration is carried out through the analysis of various
thermodynamic quantities, including heat capacity at constant
pressure, Gibbs free energy, Helmholtz free energy, and the trace of
the Hessian matrix. In order to visualize phase transitions,
identify critical points, analyzing stability and provide
comprehensive analysis, we have made the contour plot of the
mentioned thermodynamic quantities and observed that our results are
very much consistent. These investigations are conducted within the
context of exponentially corrected entropies, providing valuable
insights into the intricate thermodynamic behavior of these $5D$
charged AdS black holes under different parameter limits.

The Kramers escape rate of phase transitions for the 6-dimensional Gauss-Bonnet AdS black hole with triple phases

The Kramers escape rate of phase transitions for the 6-dimensional Gauss-Bonnet AdS black hole with triple phases

Thermodynamical topology with multiple defect curves for dyonic AdS black holes

Dyonic black holes with quasitopological electromagnetism exhibit an intriguing phase diagram with two separated first-order coexistence curves. In this paper, we aim to uncover its influence on the black hole thermodynamical topology. At first, we investigate the phase transition and phase diagram of the dyonic black holes. Comparing with previous study that there is no black hole phase transition region for a middle pressure, we find this region can narrow or disappear by fine tuning the coupling parameter. Instead, two first-order phase transitions can be observed. Importantly, we uncover that such novel phase diagram shall lead to a multiple defect curve phenomenon in black hole topology where each dyonic black hole is treated as one defect in the thermodynamical parameter space. By examining the topology, it is shown that there could be one, three, or five black hole states for given pressure and temperature. For each case, the topological number is calculated. Our results show that the topological number always takes value of +1, keeping unchanged even when the multiple defect curves appear. Therefore, our study provides an important ingredient on understanding the black hole thermodynamical topology.

Complexity growth for AdS black holes inthe presence of backreaction

Abstract We investigate the holographic complexity in the backreacted
gravity backgrounds according to the complexity-action conjecture.
The backreaction considered here is from the presence of static
strings evenly distributed over the system. We exploit a probe
string in the bulk and evaluate the Nambu-Goto action and its
dependence on backreaction. The results suggest that for slower
strings the complexity increases with the increasing of
backreaction, in accordance with the findings of the holographic
entanglement entropy. While for faster strings, the situation is
different. Furthermore, we analyze the relation between the
complexity and the space dimension as well as the string velocity.

Schottky Anomaly of Reissner-Nordstr"{o}m-de Sitter spacetime

Abstract In the extended thermodynamics of black holes, there exists a thermodynamical pressure whose dual thermodynamical quantity is volume. Extensive studies have been conducted on the phase structure of numerous black holes, which have demonstrated striking similarities to the phase structure of various ordinary matter systems. From the comparison of the thermodynamic properties between spherically symmetric AdS black holes and ordinary thermodynamic systems we known that the isovolumetric heat capacity of the former is zero, whereas that of the latter is non-zero. It is a subject of interest for the intrinsic reason for this discrepancy. For the Reissner-N"{o}rdstrom-de Sitter (RN-dS) spacetime with the coexistence of the black hole and cosmological horizons the effective thermodynamic quantities as well as the interaction between two horizons are presented. The heat capacity in the Reissner-N"{o}rdstrom-de Sitter (RN-dS) spacetime is then investigated, and it is demonstrated that the behavior of the heat capacity in the RN-dS spacetime is analogous to that of Schottky specific heat. Treating two horizons in the RN-dS spacetime as two distinct energy levels in a two-energy-level system we investigate the thermodynamic properties in the RN-dS spacetime with the method of studying the thermodynamic properties in an ordinary two-energy system, thereby elucidating the intrinsic reasons for the occurrence of Schottky specific heat in the RN-dS spacetime. The heat capacity observed in the RN-dS spacetime is not only consistent with that of the Schottky specific heat described by the effective thermodynamic quantities in the RN-dS spacetime, but also with that of an ordinary two-energy-level system. These results not only reveal the quantum properties of the RN-dS spacetime, but also provide a new avenue for further in-depth study of the quantum properties of black holes and dS spacetime.

Holographic thermal correlators and quasinormal modes from semiclassical Virasoro blocks

Motivated by its relevance for thermal correlators in strongly coupled holographic CFTs, we refine and further develop a recent exact analytic approach to black hole perturbation problem, based on the semiclassical Virasoro blocks, or equivalently via AGT relation, the Nekrasov partition functions in the Nekrasov-Shatashvili limit. Focusing on asymptotically AdS5 black hole backgrounds, we derive new universal exact expressions for holographic thermal two-point functions, both for scalar operators and conserved currents. Relatedly, we also obtain exact quantization conditions of the associated quasinormal modes (QNMs). Our expressions for the holographic CFT4 closely resemble the well-known results for 2d thermal CFTs on ℝ1,1. This structural similarity stems from the locality of fusion transformation for Virasoro blocks. We provide numerical checks of our quantization conditions for QNMs. Additionally, we discuss the application of our results to understand specific physical properties of QNMs, including their near-extremal and asymptotic limits. The latter is related to a certain large-momentum regime of semiclassical Virasoro blocks dual to Seiberg-Witten prepotentials.

Island in warped AdS black holes

This paper investigates the Page curve in warped anti-de Sitter black holes using the “quantum extremal surface” prescription. The findings reveal that in the absence of an island, the entanglement entropy of Hawking radiation grows proportionally with time and becomes divergent at later times. However, when considering the island’s emergence, which extends slightly beyond the event horizon, the growth of the entanglement entropy of Hawking radiation comes to a constant value. Eventually, the constant value is precisely twice the Bekenstein–Hawking entropy. We have also discussed the Page time and the scrambling time.

Effect of scalar condensation on fermionic pole-skipping

In this paper, we investigated the holographic fermionic pole-skipping phenomena for a class of interacting theory in a charged AdS black hole background. We have studied two types of fermion-scalar interactions in the bulk: dipole and Yukawa type interaction. Depending upon the interaction we introduced both real and charged scalar fields. We have particularly analyzed the effect of scalar condensation on the fermionic pole-skipping points and discussed their behaviour near critical temperatures.

Holographic thermodynamics of a charged AdS black hole with a global monopole

By regarding the Newton constant G N and cosmological constant Λ as variables, in this paper we study the thermodynamics and phase transition of the Reissner-Nordstr öm anti-de Sitter (RN-AdS) black hole with a global monopole within the framework of AdS/CFT correspondence. We find interesting critical phenomena and phase behavior in the (grand) canonical ensembles of fixed ( Q˜,V,C ), ( Φ˜,V,C ) and ( Q˜,V,μ ). When the other parameters are fixed, the free energy decreases with the global monopole increases. In the ( Q˜,V,C ) ensemble, the range of the unstable region decreases with the increase of the global monopole. In the ( Φ˜,V,C ) ensemble, when Φ˜<Φc , the free energy appears as two branches, where the upper and lower branches correspond to low and high entropy, respectively. When ( Q˜,V,μ ) is fixed, a new zero-order phase transition occurs in the high-entropy phase and the low-entropy phase at certain μ-dependent temperatures. When μ increases to a certain value, this zero-order phase transition disappears. This certain value is negatively related to the magnitude of the global monopole. Finally, we find that p−V criticality does not appear with the change of global monopole. Therefore, it is important to note that the CFT states of charged black holes with global monopoles do not correspond to van der Waals fluids. Finally, we find that charged black holes with global monopoles can better reflect thermodynamic phase transitions and critical phenomena under the AdS/CFT correspondence. By adjusting the change of the global monopole, the thermodynamic phase transition will also change.

Hayward–Letelier Black Holes in AdS Spacetime

We analyze Hayward black holes (BHs) with a negative cosmological constant surrounded by a cloud of strings, which we designate Hayward–Letelier AdS BHs. These solutions can be obtained by coupling the Einstein equations with nonlinear electrodynamics and the energy–momentum tensor of clouds of strings. We show that these solutions are no longer regular and have a curvature singularity at the center. In turn, we analyze the thermodynamics associated with these BHs by establishing the form of the Smarr formula and the first law of thermodynamics. We derive the expressions for the thermodynamic quantities such as pressure, temperature, heat capacity, Gibbs free energy, and isothermal compressibility. We explore the phase structure of these solutions by analyzing the behavior of the heat capacity and Gibbs free energy. These solutions exhibit a first-order phase transition, similar to van der Waals fluids. We also check the behavior of the thermodynamic quantities near the critical points and calculate the values of the critical exponents. This illustrates a robust analogy between our solutions and van der Waals fluids.

Revisiting thermodynamic topology of Hawking-Page and Davies type phase transitions

In this work, we propose a common vector field to study the thermodynamic topology of the Davies type and Hawking-Page phase transitions. Existing literature has shown that studying these two types of phase transitions typically requires defining two separate vector fields. In our approach, we adopt Duan's ϕ-mapping topological current theory to define a novel vector field, denoted as ϕ, whose critical points exactly correspond to the Davies point and the Hawking-Page phase transition point. More importantly, we can differentiate between these two points by their topological charge. While, the topological charge for the critical point corresponding to the Davies-type phase transition is found to be −1, the same for the Hawking-Page phase transition point, it is +1. Although our analysis is applicable to all black hole systems where both types of phase transitions are found, we illustrate it using three simple systems as examples: the Schwarzschild AdS black hole, the Reissner-Nordström AdS black hole in the grand canonical ensemble, and finally the Kerr AdS black holes in the grand canonical ensemble. It is well-known that these black holes exhibit both Davies and Hawking-Page phase transitions. With our proposed vector ϕ, the critical points obtained for these three systems exactly match the Davies-type and Hawking-Page phase transition points, and the associated topological charges are found to be −1 for the Davies point and +1 for the Hawking-Page phase transition point.

Thermodynamics of AdS-Schwarzschild-like black hole in loop quantum gravity

We obtained the metric of the Schwarzschild-like black hole with loop quantum gravity (LQG) corrections in anti-de Sitter (AdS) space-time, under the assumption that the cosmological constant is decoupled in LQG. We investigated its thermodynamics, including the equation of state, criticality, heat capacity, and Gibbs free energy. The P-v graph was plotted, and the critical behavior was calculated. It was found that, due to the LQG effect, the quantum-corrected Schwarzschild-AdS black hole exhibits a critical point and a critical ratio of 7/18, which differs from the Reissner–Nordstro¨m-AdS black hole’s ratio of 3/8 (the same as that of the Van der Waals system) slightly. However, there are still some similarities compared to the Van der Waals system, such as the same critical exponents and a similar P-v graph. Moreover, it is concluded that the energy-momentum tensor related to the black hole’s mass could violate the conventional first law of thermodynamics. This modified first law may violate the conservation of Gibbs free energy during the small black hole-large black hole phase transitions, potentially indicating the occurrence of the zeroth-order phase transition. The Joule–Thomson expansion was also studied. Interestingly, compared to the Schwarzschild-AdS black hole, the LQG effect leads to inversion points. The inversion curve divides the P,T coordinate system into two regions: a heating region and a cooling region, as shown in detail by the inversion curves and isenthalpic curves. The results indicated that there is a minimum inversion mass, below which any black hole will not possess an inversion point.

Particle motion and thermal fluctuations of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state

This study explores the intricate relationships between thermodynamic properties and particle dynamics of charged AdS black holes, emphasizing the impacts of charge Q and higher-order corrections, particularly the parameter β, which is a modified Chaplygin gas parameter. Our analysis of entropy reveals that smaller black holes exhibit decreasing entropy variations with increased β, while larger black holes display a complex behavior characterized by initial entropy increases followed by decreases as the horizon radius expands. The Helmholtz free energy analysis suggests that higher-order corrections significantly modify energy behavior, indicating potential phase transitions influenced by gravitational forces, with increasing β values counteracting instability linked to larger charges. Internal energy assessments show an evolving stability of black holes, transitioning from negative to positive values as entropy increases, while also highlighting the destabilizing effects of electric charge. The specific heat analysis illustrates a complex thermal stability regime, where a rise in specific heat with increasing Q correlates with greater stability. However, critical points of instability arise with higher B values, where B is the BH model parameter. Moreover, the trajectories of particles around non-rotating charged black holes reveal that lower parameters result in unbounded motion. In contrast, higher parameters tend to restrict particles closer to the event horizon. Collectively, these findings underscore the complex interplay among charge, higher-order corrections, and stability in black hole thermodynamics, shedding light on the fundamental mechanisms governing black hole behavior and paving the way for future explorations using advanced models and simulations.

The phase transition of 4D Yang–Mills charged GB AdS black hole with cloud of strings

In this paper, we present an exact spherically symmetric and Yang–Mills charged AdS black hole solution in the context of [Formula: see text] Einstein–Gauss–Bonnet (EGB) gravity in the presence of a cloud of strings. The regularity of the solution is checked. Thermodynamics of this solution is studied. The critical behavior, the types of phase transitions in canonical ensemble, the Joule–Thomson expansion, the Clapeyron equation and the critical exponents shall be investigated.

The effect of resummation on retarded Green’s function and greybody factor in AdS black holes

We investigate the retarded Green’s function and the greybody factor in asymptotically AdS black holes. Using the connection coefficients of the Heun equation, expressed in terms of the Nekrasov-Shatashvili (NS) free energy of an SU(2) supersymmetric gauge theory with four fundamental hypermultiplets, we derive asymptotic expansions for both the retarded Green’s function and the greybody factor in the small horizon limit. Furthermore, we compute the corrections to these asymptotic expansions resulting from the resummation procedure of the instanton part of the NS function.

Influences of modified Chaplygin dark fluid around a black hole

In this work, we study a static, spherically charged AdS black hole within a modified cosmological Chaplygin gas (MCG), adhering to the calorific equation of state, as a unified dark fluid model of dark energy and dark matter. We explore the influence of model parameters on several characteristics of the MCG-motivated charged AdS black hole (MCG-AdSBH), including the geodesic structure and some astrophysical phenomena such as null trajectories, shadow silhouettes, light deflection angles, and the determination of greybody bounds. We then discuss how the model parameters affect the Hawking temperature, remnant radius, and evaporation process of the MCG-AdSBH. Quasinormal modes are also investigated using the eikonal approximation method. Constraints on the MCG-AdSBH parameters are derived from EHT observations of M87* and Sgr A*, suggesting that MCG-AdSBH could be strong candidates for astrophysical black hole.

Joule-Thomson expansion, motion of particles and QPOs around Bardeen-AdS black hole immersed in a fluid of strings

In this work, we investigate the dynamics of particles around a Bardeen AdS black hole immersed in a fluid of strings, focusing on how the black hole parameters affect particle motion. We observe the black hole's Joule-Thomson expansion and the impact of physical parameters on the cooling and heating zones. Using Joule-Thomson coefficients, we also discuss the stable and unstable configuration of the considered black hole for both cases. The stability of circular equatorial orbits is analyzed using the effective potential approach. We derive analytical expressions for the energy and angular momentum of these circular orbits as functions of the black hole parameters. We also explore the impact of these parameters on the innermost stable circular orbits and discuss the effective forces acting on the particles. In addition, we examine the epicyclic oscillations of particles near a stable equatorial orbits and calculate the corresponding oscillation frequencies as function of black hole parameters. The periastron frequency is also analyzed. Furthermore, we study particle collisions and the resulting center of mass-energy in the vicinity of the black hole. We show that the parameters of the model significantly influence particle motion. Lastly, we compare the particle dynamics around the Bardeen AdS black hole immersed in a fluid of strings with those around the Bardeen black hole and the Bardeen Reissner-Nordström black hole.

Mathematical formalism of Joule-Thomson process for ADS-RN black hole coupled with non-linear electrodynamics field

We analyze the thermodynamic potentials and Joule-Thomson adiabatic expansion of a nonlinear electrodynamics charged AdS black hole. The negative cosmological constant is designated as thermodynamic pressure, while the geometrical mass is regarded as the enthalpy. In this study, we demonstrate the analogy between thermodynamic phase transitions in our considered black hole and Reissner-Nordstrom black hole systems, as well as discuss the influence of coupling parameters. The study confirmed the validity of the first law of black hole thermodynamics and the Smarr relation. We have established the Joule-Thomson thermodynamic coefficient and inversion temperature to conduct an analysis of Joule-Thomson adiabatic expansion. Also, the impact of charge parameters and nonlinear electrodynamic parameters on inversion curves have been investigated in detail. The isenthalpic and inversion curves are depicted to determine the cooling and heating regions, explicitly.