Anti-de Sitter Black Holes Research Articles

The Hawking\u2013Page phase transitions in the extended phase space in the Gauss\u2013Bonnet gravity

In this paper, the Hawking–Page phase transitions between the black holes and thermal anti-de Sitter (AdS) space are studied with the Gauss–Bonnet term in the extended phase space, in which the varying cosmological constant plays the role of an effective thermodynamic pressure. The Gauss–Bonnet term exhibits its effects via introducing the corrections to the black hole entropy and Gibbs free energy. The global phase structures, especially the phase transition temperature T_{mathrm{HP}} and the Gibbs free energy G, are systematically investigated, first for the Schwarzschild–AdS black holes and then for the charged and rotating AdS black holes in the grand canonical ensembles, with both analytical and numerical methods. It is found that there are terminal points in the coexistence lines, and T_{mathrm{HP}} decreases at large electric potentials and angular velocities and also decreases with the Gauss–Bonnet coupling constant alpha .

Nonlinear electrodynamics generalization of the rotating BTZ black hole

We obtain two exact solutions of Einstein gravity coupled to nonlinear electrodynamics (NLED) in ($2+1$)-dimensional anti--de Sitter (AdS) spacetime. The solutions are characterized by the mass $M$, angular momentum $J$, cosmological constant or (anti) de Sitter parameter $\mathrm{\ensuremath{\Lambda}}$, and an electromagnetic parameter $Q$, that is related to an electric field in the first solution and to a magnetic charge for the second solution. Depending on the range of the parameters, the solutions admit a charged rotating asymptotically AdS black hole (BH) interpretation or a charged rotating asymptotically AdS traversable wormhole (WH). If the electromagnetic field is turned off, the stationary Ba\~nados-Teitelboim-Zanelli (BTZ) BH is recovered; in such a way that our BH-WH solutions are nonlinear charged generalizations of the stationary BTZ-BH. Moreover, in contrast to the BTZ metric, the derived AdS solutions are singular at certain radius ${r}_{s}\ensuremath{\ne}0$, resembling the ring singularity of the Kerr-Newman spacetime; while if $\mathrm{\ensuremath{\Lambda}}$ is positive the curvature invariants of the second solution are finite.

Interface in AdS black hole spacetime

Abstract We consider a defect solution in the anti-de Sitter (AdS) black hole spacetime. This is a generalization of the previous work [K. Nagasaki et al., J. High Energy Phys. 1201, 139 (2012)] to another spacetime. This system consists of D3- and D5-branes. The equation of motion for a sort of nonlocal operator, an “interface”, is given and its numerical solution is shown by the numerical calculation. We also consider a string extending between this interface and the boundary of the AdS spacetime. This corresponds to the quark–interface potential in the boundary theory of the bulk black hole spacetime. This result gives a new example of a holographic relation that includes the gauge flux in the probe D5-brane.

Critical Phenomena of Charged AdS Black Holes in Rastall Gravity

We construct analytical charged anti-de Sitter (AdS) black holes surrounded by perfect fluids in four dimensional Rastall gravity. Then, we discuss the thermodynamics and phase transitions of charged AdS black holes immersed in regular matter like dust and radiation, or exotic matter like quintessence, ΛCDM type, and phantom fields. Surrounded by phantom field, the charged AdS black hole demonstrates a new phenomenon of reentrant phase transition (RPT) when the parameters Q, Np, and ψ satisfy some certain condition, along with the usual small/large black hole (SBH/LBH) phase transition for the surrounding dust, radiation, quintessence, and cosmological constant fields.

Phase Structure and Quasinormal Modes of AdS Black Holes in Rastall Theory

We discuss the P−V criticality and phase transition in the extended phase space of anti-de Sitter(AdS) black holes in four-dimensional Rastall theory and recover the Van der Waals (VdW) analogy of small/large black hole (SBH/LBH) phase transition when the parameters ωs and ψ satisfy some certain conditions. Later, we further explore the quasinormal modes (QNMs) of massless scalar perturbations to probe the SBH/LBH phase transition. It is found that it can be detected near the critical point, where the slopes of the QNM frequencies change drastically in small and large black holes.

Minimal Length Effect on Thermodynamics and Weak Cosmic Censorship Conjecture in Anti-de Sitter Black Holes via Charged Particle Absorption

In this paper, we investigate the minimal length effects on the thermodynamics and weak cosmic censorship conjecture in a RN-AdS black hole via charged particle absorption. We first use the generalized uncertainty principle (GUP) to investigate the minimal length effect on the Hamilton-Jacobi equation. After the deformed Hamilton-Jacobi equation is derived, we use it to study the variations of the thermodynamic quantities of a RN-Ads black hole via absorbing a charged particle. Furthermore, we check the second law of thermodynamics and the weak cosmic censorship conjecture in two phase spaces. In the normal phase space, the second law of thermodynamics and the weak cosmic censorship conjecture are satisfied in the usual and GUP-deformed cases, and the minimal length effect makes the increase of entropy faster than the usual case. After the charge particle absorption, the extremal RN-AdS black hole becomes nonextremal. In the extended phase space, the black hole entropy can either increase or decrease. When T>2Pr+, the second law is satisfied. When T<2Pr+, the second law of thermodynamics is violated for the extremal or near-extremal black hole. Finally, we find that the weak cosmic censorship conjecture is legal for extremal and near-extremal RN-Ads black holes in the GUP-deformed case.

AdS4 black holes with nonlinear source in rainbow gravity

We explore new four-dimensional black holes, with the Einstein-Λ theory coupled to nonlinear electrodynamics, in an energy-dependent spacetime. By considering the power-law model of nonlinear electrodynamics and solving the coupled field equations, with properly fixing the parameters of the theory, we obtain two new classes of nonlinearly charged black holes with anti-de Sitter (AdS) asymptote. With the aim of studying the thermodynamic properties of the novel AdS black holes, we calculate the conserved and thermodynamic quantities such as black hole mass, electric charge, electric potential, temperature, and entropy in the presence of rainbow functions. Although some of these quantities are affected by the rainbow functions, interestingly, they satisfy the first law of black hole thermodynamics in its standard form. Based on the canonical ensemble method and by calculating the black hole heat capacity, we analyze the black hole local stability or thermodynamic phase transitions. The horizon radius of those black holes which experience type one or type two phase transition as well as the conditions under which the black holes remain stable are determined. Finally, via consideration of black hole thermal fluctuations, we examine the impacts of quantum gravitational corrections on the thermodynamic properties of our new AdS rainbow black holes.

Correction to the tunneling radiation of arbitrary spin fermions in Kerr Anti-de Sitter black hole

According to the dispersion relation that stems from the string theory and the quantum gravitational theory, we study the dynamic equation of fermions, that is Rarita–Schwinger equation. Based on the Lorentz dispersion relation modified in the high-energy case, the dynamic equation of arbitrary spin fermions is accurately corrected in the Kerr Anti-de Sitter black hole, then the action of fermions with arbitrary spin is computed. To do so, we obtain the new expressions for tunneling rate, Hawking temperature and entropy of the black hole. At last, some comments are made on the results of our work.

Probing correlation between photon orbits and phase structure of charged AdS black hole in massive gravity background

The phase structure of charged anti-de Sitter black hole in massive gravity is investigated using the unstable circular photon orbits formalism, concretely we establish a direct link between the null geodesics and the critical behavior thermodynamic of such black hole solution. Our analysis reveals that the radius and the impact parameter corresponding to the unstable circular orbits can be used to probe the thermodynamic phase structure. We also show that the latter are key quantities to characterize the order of Van der Waals-like phase transition. Namely, we found a critical exponent around [Formula: see text]. All these results support further that the photon trajectories can be used as a useful and crucial tool to probe the thermodynamic black holes criticality.

Contact geometry and thermodynamics of black holes in AdS spacetimes

In this paper we discuss a formulation of extended phase space thermodynamics of black holes in Anti de Sitter (AdS) spacetimes from the contact geometry point of view. Thermodynamics of black holes can be understood within the framework of contact geometry as flows of vector fields generated by Hamiltonian functions on equilibrium submanifolds in the extended phase space that naturally incorporates the structure of a contact manifold. Deformations induced by the contact vector fields are used to construct various maps among thermodynamic quantities. Thermodynamic variables and equations of state of Schwarzschild black holes are mapped to that of Reissner-Nordstr\"{o}m black holes in AdS, with charge as the deformation parameter. In addition, the equations of state of general black holes in AdS are shown to emerge from the high-temperature ideal gas limit equations via suitable deformations induced by contact vector fields. The Hamilton-Jacobi formalism analogous to mechanics is set up, and the corresponding characteristic curves of contact vector fields are explicitly obtained to model thermodynamic processes of black holes. Extension to thermodynamic cycles in this framework is also discussed.

The bound on chaos for closed strings in Anti-de Sitter black hole backgrounds

We perform a systematic study of the maximum Lyapunov exponent values λ for the motion of classical closed strings in Anti-de Sitter black hole geometries with spherical, planar and hyperbolic horizons. Analytical estimates from the linearized varia- tional equations together with numerical integrations predict the bulk Lyapunov exponent value as λ ≈ 2πTn, where n is the winding number of the string. The celebrated bound on chaos stating that λ ≤ 2πT is thus systematically modified for winding strings in the bulk. Within gauge/string duality, such strings apparently correspond to complicated operators which either do not move on Regge trajectories, or move on subleading trajectories with an unusual slope. Depending on the energy scale, the out-of-time-ordered correlation functions of these operators may still obey the bound 2πT, or they may violate it like the bulk exponent. We do not know exactly why the bound on chaos can be modified but the indication from the gauge/string dual viewpoint is that the correlation functions of the dual gauge operators never factorize and thus the original derivation of the bound on chaos does not apply.

Field-theoretical construction of currents and superpotentials in Lovelock gravity

Conserved currents and related superpotentials for perturbations on arbitrary backgrounds in the Lovelock theory are constructed. We use the Lagrangian based field-theoretical method where perturbations are considered as dynamical fields propagating on a given background. Such a formulation is exact (not approximate) and equivalent to the theory in the original metric form. From the very start, using Noether theorem, we derive the Noether–Klein identities and adopt them for the purposes of the current work. Applying these identities in the framework of Lovelock theory, we construct conserved currents, energy-momentum tensors out of them, and related superpotentials with arbitrary displacement vectors, not restricting to Killing vectors. A comparison with the well known Abbott–Deser–Tekin approach is given. The developed general formalism is applied to give conserved quantities for perturbations on anti-de Sitter (AdS) backgrounds. As a test we calculate mass of the Schwarzschild–AdS black hole in the Lovelock theory in arbitrary D dimensions. Proposals for future applications are presented.

Petrov type D equation on horizons of nontrivial bundle topology

We consider $3$-dimensional isolated horizons (IHs) generated by null curves that form nontrivial $U(1)$ bundles. We find a natural interplay between the IH geometry and the $U(1)$-bundle geometry. In this context we consider the Petrov type D equation introduced and studied in previous works \cite{DLP1,DLP2,LS,DKLS1}. From the $4$-dimensional spacetime point of view, solutions to that equation define isolated horizons embeddable in vacuum spacetimes (with cosmological constant) as Killing horizons to the second order such that the spacetime Weyl tensor at the horizon is of the Petrov type D. From the point of view of the $U(1)$-bundle structure, the equation couples a $U(1)$-connection, a metric tensor defined on the base manifold and the surface gravity in a very nontrivial way. We focus on the $U(1)$-bundles over $2$-dimensional manifolds diffeomorphic to $2$-sphere. We have derived all the axisymmetric solutions to the Petrov type D equation. For a fixed value of the cosmological constant they set a $3$-dimensional family as one could expect. A surprising result is, that generically our horizons are not embeddable in the known exact solutions to Einstein's equations. It means that among the exact type D spacetimes there exists a new family of spacetimes that generalize the properties of the Kerr- (anti) de Sitter black holes on one hand and the Taub-NUT spacetimes on the other hand.

Localized thermal states and negative energy

We construct localized states defined in a ball or the half-space of a conformal field theory (CFT) in Minkowski that are thermal with respect to the local modular flow. We compute their energy density at arbitrary temperature for a variety of CFTs, and find values for which it is negative and divergent at the boundary. Despite this singular behavior we show that the energy measured by an observer is consistent with the bounds present in the literature. For holographic CFTs these states are captured by hyperbolic black holes in anti-de Sitter, where the negative energy in field theory amounts to the well known negative mass of the black hole. As a byproduct, we show that the Casini-Huerta-Myers proof of the Ryu-Takayangi holographic entanglement formula for the vacuum reduced to a ball can be naturally extended to include half-space regions.

Linearized stability of Bardeen anti-de Sitter wormholes

In this paper, we explore the stable and unstable geometrical structures of thin-shell wormholes. We use Visser cut and paste approach to develop thin-shell from Bardeen anti-de Sitter black holes. The characteristics of matter distribution are determined by using Israel formalism. We discuss the existence of exotic matter at the wormhole throat through energy conditions and examine the attractive/repulsive nature of wormhole throat. The linearized stability of thin-shell is studied through barotropic and variable equations of state (generalized phantomlike and generalized Chaplygin gas model). We conclude that the stability of wormhole depends on the matter distribution as well as cosmological constant. Finally, we compare the stable structure of wormhole for these equations of state through length parameter.

Extended quasilocal Thermodynamics of Schwarzchild–anti de Sitter black holes

In this work we study a homogeneous and quasilocal Thermodynamics associated to the Schwarzschild–anti de Sitter black hole. The usual thermodynamic description is extended within a Hamiltonian approach with the introduction of the cosmological constant in the thermodynamic phase space. The macroscopic treatment presented is consistent in as much as it respects the laws of black hole Thermodynamics and accepts the introduction of any thermodynamic potential. We are able to construct new equations of state that characterize the Thermodynamics. Novel phenomena can be expected from the proposed setup.

Information versus stability in an anti-de Sitter black hole

Information entropies associated with the energy density in position and momentum spaces are build for an anti-de Sitter (AdS) black hole. These quantities, that satisfy an entropic uncertainty relation, vary with the temperature. The higher is the black hole temperature, the greater/smaller is the information encoded respectively in the position/momentum distributions of energy. On the other hand, as it is well known, AdS black holes are subject to the Hawking Page phase transition. The amplitude for dominance of the black hole phase over the thermal AdS phase increases with the temperature. So, as the system becomes more stable, there is a change in the way that information is stored. In particular: information stored in the spatial energy density increases while information stored in the energy density in momentum space decreases.

Thermal corrections of Born–Infeld–anti-de Sitter black hole in massive gravity

The impact of thermal fluctuations on the thermodynamics of Born–Infeld–anti-de Sitter black hole is being investigated. For this purpose, we analyze the consequences of logarithmic corrections on thermodynamics potentials like Helmholtz and Gibbs. We find out the relations for critical points and stability and observe that thermal corrections play a vital role in them.

Hawking Effect of AdS2 Black Holes in the Jackiw-Teitelboim Model

It might be tempting to consider that the two-dimensional anti-de Sitter black hole in the Jackiw-Teitelboim model is thermally hot by invoking the non-vanishing surface gravity. So, one might expect that the local temperature would also be blue-shifted near the horizon, while it would vanish at infinity because of the Tolman factor of the local temperature. In this paper, we will show that the local temperature vanishes everywhere, which respects the equivalence principle perfectly in contrast to the case of the asymptotically flat black holes recovering the equivalence principle just at the horizon. In other words, the origin of radiation for a fixed observer comes from the Unruh effect rather than the Hawking effect. If the inward and outward fluxes are defined non-trivially at the horizon, then the local temperature of the black hole takes the usual Tolman form; however, the divergent Tolman temperature at the horizon is incompatible with the finite local energy density there.

Holographic paramagnetic-ferromagnetic phase transition with Power-Maxwell electrodynamics

We explore the effects of Power-Maxwell nonlinear electrodynamics on the properties of holographic paramagnetic-ferromagnetic phase transition in the background of Schwarzchild Anti-de Sitter (AdS) black hole. For this purpose, we introduce a massive 2−form coupled to the Power-Maxwell field. We perform the numerical shooting method in the probe limit by assuming the Power-Maxwell and the 2−form fields do not back react on the background geometry. We observe that increasing the strength of the power parameter causes the formation of magnetic moment in the black hole background harder and critical temperature lower. In the absence of external magnetic field and at the low temperatures, the spontaneous magnetization and the ferromagnetic phase transition happen. In this case, the critical exponent for magnetic moment is always 1/2 which is in agreement with the result from the mean field theory. In the presence of external magnetic field, the magnetic susceptibility satisfies the Cure-Weiss law.