Asymptotically Anti-de Sitter Research Articles

De Sitter space is sometimes not empty

Multiple lines of evidence suggest that the Hilbert space of an isolated de Sitter universe is one dimensional but can appear larger when probed by a gravitating observer. To test this idea, we compute the von Neumann entropy of a field theory in a two-dimensional de Sitter universe which is entangled in a thermal-like state with the same field theory on a disjoint, asymptotically anti-de Sitter (AdS) black hole. Previously, it was shown that the replica trick for computing the entropy of such entangled gravitating systems requires the inclusion of a non-perturbative effect in quantum gravity — novel wormholes connecting the two spaces. Here we show that: (a) the expected wormholes connecting de Sitter and AdS universes exist, avoiding a no-go theorem via the presence of sources on the AdS boundary; (b) the entanglement entropy vanishes if the nominal entropy of the de Sitter cosmological horizon SdS=AhorizondS/4GN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\left({S}_{\ extrm{dS}}={A}_{\ extrm{horizon}}^{\ extrm{dS}}/4{G}_{\ extrm{N}}\\right) $$\\end{document} is less than the entropy of the AdS black hole horizon SBH=AhorizonAdS/4GN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\left({S}_{\ extrm{BH}}={A}_{\ extrm{horizon}}^{\ extrm{AdS}}/4{G}_{\ extrm{N}}\\right) $$\\end{document}, i.e., SdS< SBH; (c) the entanglement entropy is finite when SdS > SBH. Thus, the de Sitter Hilbert space is effectively nontrivial only when SdS > SBH. The AdS black hole we introduce can be regarded as an “observer” for de Sitter space. In this sense, our result is a non-perturbative generalization of the recent perturbative argument that the algebra of observables on the de Sitter static patch becomes nontrivial in the presence of an observer.

Entropy Bounds for Rotating AdS Black Holes.

We propose novel thermodynamic inequalities that apply to stationary asymptotically anti-de Sitter (AdS) black holes. These inequalities incorporate the thermodynamic volume and refine the reverse isoperimetric inequality. To assess the validity of our conjectures, we apply them to a wide range of analytical black hole solutions, observing compelling evidence in their favor. Intriguingly, our findings indicate that these inequalities may also apply for black holes of nonspherical horizon topology, as we show their validity as well for thin asymptotically AdS black rings.

Quasi-local black hole thermodynamics and gravitational pressure

Black hole thermodynamics, in which physical quantities are global, is well established. In realistic astrophysical processes, the quasi-local black hole thermodynamics (thermodynamics in a finite spacetime region) is an essential problem. We develop quasi-local black hole thermodynamics by using the quasi-local energies of gravitation. For the first time, we suggest the concept of gravitational pressure, i.e. the pressure of gravitational field itself in thermodynamics for black holes, and find that it is necessary for quasi-local black hole thermodynamics in asymptotic flat space. We extend quasi-local black hole thermodynamics to the cases of asymptotic de Sitter and anti-de Sitter spaces. This exploration presents new insights into quasi-local energy of gravity, and is much more closely related to realistic astrophysics.

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 .

A note on the entanglement entropy of primary fermion fields in JT gravity* *Supported by the National Natural Science Foundation of China (11975116)

In this paper we analyze and discuss 2D Jackiw-Teitelboim (JT) gravity coupled to primary fermion fields in asymptotically anti-de Sitter (AdS) spacetimes. We obtain a particular solution of the massless Dirac field outside the extremal black hole horizon and find the solution for the dilaton in JT gravity. As two dimensional JT gravity spacetime is conformally flat, we calculate the two point correlators of primary fermion fields under the Weyl transformations. The primary goal of this work is to present a standard technique, called resolvent, rather than using CFT methods. We redefine the fields in terms of the conformal factor as fermion fields and use the resolvent technique to derive the renormalized entanglement entropy for massless Dirac fields in JT gravity.

Penrose Inequality as a Constraint on the Low Energy Limit of Quantum Gravity

We construct initial data violating the anti-de Sitter Penrose inequality using scalars with various potentials. Since a version of the Penrose inequality can be derived from AdS/CFT, we argue that it is a new swampland condition, ruling out holographic UV completion for theories that violate it. We produce exclusion plots on scalar couplings violating the inequality, and we find no violations for potentials from string theory. In the special case where the dominant energy condition holds, we use general relativity techniques to prove the anti-de Sitter (AdS) Penrose inequality in all dimensions, assuming spherical, planar, or hyperbolic symmetry. However, our violations show that this result cannot be generically true with only the null energy condition, and we give an analytic sufficient condition for violation of the Penrose inequality, constraining couplings of scalar potentials. Like the Breitenlohner-Freedman bound, this gives a necessary condition for the stability of asymptotically AdS (AAdS) spacetimes.

Black hole thermodynamics from logotropic fluids

We show that the Einstein field equations with a negative cosmological constant can admit black hole solutions whose thermodynamics coincides with that of logotropic fluids, recently investigated to heal some cosmological and astrophysical issues. For this purpose, we adopt the Anton–Schmidt equation of state, which represents a generalized version of logotropic fluids. We thus propose a general treatment to obtain an asymptotic anti-de Sitter metric, reproducing the thermodynamic properties of both Anton–Schmidt and logotropic fluids. Hence, we explore how to construct suitable spacetime functions, invoking an event horizon and fulfilling the null, weak, strong and dominant energy conditions. We further relax the strong energy condition to search for possible additional solutions. Finally, we discuss the optical properties related to a specific class of metrics and show how to construct an effective refractive index depending on the spacetime functions and the thermodynamic quantities of the fluid under study. We also explore possible departures with respect to the case without the fluid.

Descalarization by quenching charged hairy black hole in asymptotically AdS spacetime

In this work, we study the real-time dynamics of the charged hairy black hole with the time-dependent source of scalar field in asymptotically anti-de Sitter (AdS) spacetime. The numerical results reveal a novel descalarization mechanism. In order to obtain the hairy black hole as the initial data for the quench process, we first analyze the quasi-normal modes of the massive complex scalar field on the Reissner-Nordström anti-de Sitter (RN-AdS) black hole background. We find the dominant unstable modes for large and small RN-AdS black holes come from the zero-damped modes and AdS modes, respectively. Then, the unstable RN-AdS black holes are perturbed to trigger the transition to hairy black holes. With the hairy black hole in hand, we specify a time dependent scalar source for the system. As the source is turned on, the electric charge, energy and scalar condensation of the system start to oscillate with the entropy increasing monotonically. Finally, with the decay of the scalar source, the system gradually settles down to a new state. Interestingly, the final state of the evolution could be a hairy black hole with less scalar condensation, a RN-AdS black hole or a Schwarzschild-AdS black hole, which depends on the quench strength. However, as long as the quench strength is large enough, the system always loses all the electric charge and converges to the Schwarzschild-AdS black hole.

Anti-de Sitter neutron stars in the theory of gravity with nonminimal derivative coupling

We consider neutron star configurations in the scalar-tensor theory of gravity with the coupling between the kinetic term of a scalar field and the Einstein tensor (such the model is a subclass of Horndeski gravity). Neutron stars in this model were studied earlier for the special case with a vanishing “bare” cosmological constant, Λ0 = 0, and a vanishing standard kinetic term, α = 0. This special case is of interest because it admits so-called stealth configuration, i.e. vacuum configuration with nontrivial scalar field and the Schwarzschild metric. However, generally one has Λ0 ≠ 0 and α ≠ 0 and in this case a vacuum configuration is represented as an asymptotically anti-de Sitter (AdS) black hole solution with the nontrivial scalar field. We construct neutron star configurations in this general case and show that resulting diagrams describing the relation between mass and radius of the star essentially differ from those obtained in GR or the particular model with α = Λ0 = 0. Instead, the mass-radius diagrams are similar to those obtained for so-called bare strange stars when a star radius decreases monotonically with decreasing mass. We show also that neutron stars in the theory of gravity with nonminimal derivative coupling are more compact comparing to those in GR or the particular model with α = Λ0 = 0 and suggest a way to estimate possible values of the parameter of nonminimal coupling ℓ. At last, using the Regge-Wheeler method, we discuss briefly the stability of obtained neutron star configurations.

Higher-dimensional polytropic and modified Chaplygin black holes: Thermodynamics and heat engines

In this paper, we have assumed that the thermodynamic pressure may be generated by the negative cosmological constant and the thermodynamic parameters of the n-dimensional asymptotically Anti-de Sitter (AdS)-Tangherlini black holes are identical with the polytropic gas and modified Chaplygin gas separately. The black hole mass, volume, entropy, and temperature have been written due to the assigned gases’ thermodynamic system. We found the solutions of Einstein’s field equations of n-dimensional black hole for polytropic gas and modified Chaplygin gas. The null energy condition, weak energy condition, strong energy condition, and dominant energy condition have been examined for the fluid sources in n-dimensional black hole system due to both the gases. We found that the four energy conditions completely depend on the model parameters and the dimensions of the spacetime. We have studied the heat engine phenomena for both the black holes and analyzed the work done with the efficiencies due to the Carnot and other cycles.

Magnetically charged Euler-Heisenberg black holes with scalar hair

We study the Einstein-Euler-Heisenberg theory in the presence of a self interacting scalar field, minimally coupled to gravity. We solve analytically the field equations for the magnetically charged case and we obtain novel magnetically charged hairy black holes. The scalar field dresses the black hole with a secondary scalar hair. The hairy black hole develops three horizons when Euler-Heisenberg parameter and the magnetic charge are small and the horizon radius is getting large when the scalar charge and the gravitational mass are large. The presence of matter and the magnetic field outside the horizon of the black hole increases the temperature only for small black holes. Calculating the heat capacity we show that the asymptotically AdS Euler-Heisenberg hairy black hole undergoes a second order phase transition and then it is stabilized. Also the weak energy condition is violated for the asymptotically AdS Euler-Heisenberg hairy black hole.

Gravothermal catastrophe and critical dimension in a D -dimensional asymptotically AdS spacetime

We investigate the structure and stability of the thermal equilibrium states of a spherically symmetric self-gravitating system in a $D$-dimensional asymptotically Anti-de Sitter(AdS) spacetime. The system satisfies the Einstein-Vlasov equations with a negative cosmological constant. Due to the confined structure of the AdS potential, we can construct thermal equilibrium states without any artificial wall in the asymptotically AdS spacetime. Accordingly, the AdS radius can be regarded as the typical size of the system. Then the system can be characterized by the gravothermal energy and AdS radius normalized by the total particle number. We investigate the catastrophic instability of the system in a $D$-dimensional spacetime by using the turning point method. As a result, we find that the curve has a double spiral structure for $4\le D\le 10$ while it does not have any spiral structures for $D\ge11$ as in the asymptotically flat case confined by an adiabatic wall. Irrespective of the existence of the spiral structure, there exist upper and lower bounds for the value of the gravothermal energy. This fact indicates that there is no thermal equilibrium solution outside the allowed region of the gravothermal energy. This property is also similar to the asymptotically flat case.

The action of HRT-areas as operators in semiclassical gravity

We study the action of Hubeny-Rangamani-Takayanagi (HRT) area operators on the covariant phase space of classical solutions. It has been previously proposed that this action generates a transformation which, roughly speaking, boosts the entanglement wedge on one side of the HRT surface relative to the entanglement wedge on the other side. We give a sharp argument for a precise result of this form in a general theory of Einstein-Hilbert gravity minimally coupled to matter, taking appropriate care with asymptotically Anti-de Sitter (AdS) boundary conditions. The result agrees with direct computations of commutators involving HRT areas in pure 2+1 dimensional Einstein-Hilbert gravity on spacetimes asymptotic to planar AdS. We also clarify the sense in which this transformation is singular in the deep UV when the HRT-surface is anchored to an asymptotically AdS boundary.

Generalized Gravitational Phase Transition in Novel 4D Einstein–Gauss–Bonnet Gravity

AbstractIn this paper, the possible existence of a thermal phase transition from asymptotic anti‐de Sitter (AdS) to de Sitter (dS) geometries in vacuum in the context of the novel fourdimensional Einstein–Gauss–Bonnet (4D EGB) gravity is presented. The phase transition proceeds via a thermalon (the Euclidean section of a bubble thin shell) formation, having a black hole in the dS spacetime and a thermal AdS spacetime in the exterior, without introducing any matter field. From the analysis, it is found that, using regularized novel 4D EGB gravity, the gravitational phase transitions occur for all allowed values of the 4D EGB coupling. In the 4D EGB gravity, the existence of the above phase transition is over a narrow range of the 4D EGB coupling, with particular critical values. In contrast, in five‐dimensional (5D) EGB gravity, a 5D sector needs a wider range of its coupling for the existence of a thermalon, and there also exist critical values for the emergence of the above phase transition.

Evolution of anti–de Sitter black holes in Einstein-Maxwell-dilaton theory

We study the nonlinear evolution of the spherical symmetric black holes under a small neutral scalar field perturbation in Einstein-Maxwell-dilaton theory with coupling function $f(\phi)=e^{-b\phi}$ in asymptotic anti-de Sitter spacetime. The non-minimal coupling between scalar and Maxwell fields allows the transmission of the energy from the Maxwell field to the scalar field, but also behaves as a repulsive force for the scalar. The scalar field oscillates with damping amplitude and converges to a final value by a power law. The irreducible mass of the black hole increases abruptly at initial times and then saturates to the final value exponentially. The saturating rate is twice the decaying rate of the dominant mode of the scalar. The effects of the black hole charge, the cosmological constant and the coupling parameter on the evolution are studied in detail. When the initial configuration is a naked singularity spacetime with a large charge to mass ratio, a horizon will form soon and hide the singularity.

Maxwell perturbations in a cavity with Robin boundary conditions: two branches of modes with spectrum bifurcation on Schwarzschild black holes

We perform a systematic study of the Maxwell quasinormal spectrum in a mirror-like cavity following the generic Robin type vanishing energy flux principle, by starting with the Schwarzschild black holes in this paper. It is shown that, for black holes in a cavity, the vanishing energy flux principle leads to two different sets of boundary conditions. By solving the Maxwell equations with these two boundary conditions both analytically and numerically, we observe two distinct sets of modes. This indicates that the vanishing energy flux principle may be applied not only to asymptotically anti-de Sitter (AdS) black holes but also to black holes in a cavity. In the analytic calculations, the imaginary part of the Maxwell quasinormal modes are derived analytically for both boundary conditions, which match well with the numeric results. While in the numeric calculations, we complete a thorough study on the two sets of the Maxwell spectrum by varying the mirror radius r_m, the angular momentum quantum number ell , and the overtone number N. In particular, we proclaim that the Maxwell spectrum may bifurcate for both modes when the mirror is placed around the black hole event horizon, which is analogous to the spectrum bifurcation effects found for the Maxwell fields on asymptotically AdS black holes. This observation provides another example to exhibit the similarity between black holes in a cavity and the AdS black holes.

Jackiw-Teitelboim gravity in the second order formalism

We formulate the path integral for Jackiw-Teitelboim gravity in the second order formalism working directly with the metric and the dilaton. We consider the theory both in Anti-de Sitter(AdS) and de Sitter space(dS) and analyze the path integral for the disk topology and the “double trumpet” topology with two boundaries. We also consider its behavior in the presence of conformal matter. In the dS case the path integral evaluates the wavefunction of the universe which arises in the no-boundary proposal. In the asymptotic AdS or dS limit without matter we get agreement with the first order formalism. More generally, away from this limit, the path integral is more complicated due to the presence of modes from the gravity- dilaton sector and also matter sector with short wavelengths along the boundary that are smaller than the AdS or dS scales. In the double trumpet case, for both AdS and dS, we find that bosonic matter gives rise to a diverging contribution in the moduli space integral rendering the path integral ill-defined. The divergence occurs when the size of the wormhole neck vanishes and is related to the Casimir effect. For fermions this divergence can be avoided by imposing suitable boundary conditions. In this case, in dS space the resulting path integral gives a finite contribution for two disconnected universes to be produced by quantum tunneling.

Topological black holes in mimetic gravity

In this paper, we construct some new classes of topological black hole solutions in the context of mimetic gravity and investigate their properties. We study the uncharged and charged black holes, separately. We find the following novel results: (i) In the absence of a potential for the mimetic field, black hole solutions can address the flat rotation curves of spiral galaxies and alleviate the dark matter problem without invoking particle dark matter. Thus, mimetic gravity can provide a theoretical background for understanding flat galactic rotation curves through modifying Schwarzschild space–time. (ii) We also investigate the casual structure and physical properties of the solutions. We observe that in the absence of a potential, our solutions are not asymptotically flat, while in the presence of a negative constant potential for the mimetic field, the solutions are asymptotically anti-de Sitter (AdS). (iii) Finally, we explore the motion of massless and massive particles and give a list of the types of orbits. We study the differences of geodesic motion in the Einstein gravity and in mimetic gravity. In contrast to the Einstein gravity, massive particles always move on bound orbits and cannot escape the black hole in mimetic gravity. Furthermore, we find stable bound orbits for massless particles.

Divergence behavior of thermodynamic curvature scalar at critical point in the extended phase space of generic black holes

The P-V phase transition and critical behavior in the extended phase space of asymptotic Anti-de Sitter (AdS) black holes have been widely investigated, in which four critical exponents around critical point are found to be consistent with values in the mean field theory. Recently, another critical exponent ν related to divergent correlation length at critical point is proposed by using thermodynamic curvature scalar RN in the charged AdS black hole. In this paper, we develop a method to investigate the divergent behavior of RN at critical point, and find that the divergent behavior of RN around the critical point expresses a universal property in generic black holes. We further directly apply this method to investigate black holes in de Rham-Gabadadze-Tolley (dRGT) massive gravity to check this universality. Those results shed new lights on the microscopic properties of black holes.

Ellis wormholes in anti-de Sitter space

We construct traversable wormholes with anti-de Sitter asymptotics supported by a phantom field. These wormholes are massless and symmetric with respect to reflection of the radial coordinate eta rightarrow - eta . Their circumferential radius decreases monotonically from radial infinity to their single throat. Analogous to their asymptotically flat counterparts, these anti-de Sitter wormholes possess an unstable radial mode.