Asymptotically Anti-de Sitter Research Articles

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.

A Komar-like integral for mass and angular momentum of asymptotically AdS black holes in Einstein gravity

The purpose of this paper is to enhance the conventional Komar integral to asymptotically anti-de Sitter (AdS) black holes. In order to do so, we first obtain a potential that is the linear combination of the usual Komar potential with two third-order derivative terms generated by the action of the d’Alembertian operator and the exterior derivative upon a Killing vector. Then this higher-order corrected potential is extended to the Einstein gravity with a negative cosmological constant, yielding the potential that is the linear combination of the usual Komar one with it acted on by the d’Alembertian. It is demonstrated that the surface integral of the improved Komar potential can serve as a formula for conserved charges of asymptotically AdS spacetimes. Finally, to illustrate such a formula, we make use of it to compute the mass and the angular momentum of Schwarzschild-AdS black holes, regular AdS black holes, asymptotically AdS Kerr-Sen black holes, Kerr-NUT-AdS black holes, and Kerr-AdS black holes in arbitrary dimensions. The results are in agreement with the ones in the literature.

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

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

Validity of thermodynamic laws and weak cosmic censorship for AdS black holes and black holes in a cavity * *Supported in part by National Natural Science Foundation of China (11875196, 11375121, 11005016)

By throwing a test charged particle into a Reissner-Nordstrom (RN) black hole, we test the validity of the first and second laws of thermodynamics and the weak cosmic censorship conjecture (WCCC) with two types of boundary conditions: the asymptotically anti-de Sitter (AdS) space and a Dirichlet cavity wall placed in an asymptotically flat space. For the RN-AdS black hole, the second law of thermodynamics is satisfied, and the WCCC is violated for both extremal and near-extremal black holes. For the RN black hole in a cavity, the entropy can either increase or decrease depending on the change in the charge, and the WCCC is satisfied/violated for the extremal/near-extremal black hole. Our results indicate that there may be a connection between the black hole thermodynamics and the boundary condition imposed on the black hole.

Topological or rotational non-Abelian gauge fields from Einstein-Skyrme holography

We report analytically known states at non-zero temperature which may serve as a powerful tool to reveal common topological and thermodynamic properties of systems ranging from the QCD phase diagram to topological phase transitions in condensed matter materials. In the holographically dual gravity theory, these are analytic solutions to a five-dimensional non-linear-sigma (Skyrme) model dynamically coupled to Einstein gravity. This theory is shown to be holographically dual to mathcal{N} = 4 Super-Yang-Mills theory coupled to an SU(2)-current. All solutions are fully backreacted asymptotically Anti-de Sitter (AdS) black branes or holes. One family of global AdS black hole solutions contains non-Abelian gauge field configurations with positive integer Chern numbers and finite energy density. Larger Chern numbers increase the Hawking-Page transition temperature. In the holographically dual field theory this indicates a significant effect on the deconfinement phase transition. Black holes with one Hawking temperature can have distinct Chern numbers, potentially enabling topological transitions. A second family of analytic solutions, rotating black branes, is also provided. These rotating solutions induce states with propagating charge density waves in the dual field theory. We compute the Hawking temperature, entropy density, angular velocity and free energy for these black holes/branes. These correspond to thermodynamic data in the dual field theory. For these states the energy-momentum tensor, (non-)conserved current, and topological charge are interpreted.

Echoes of compact objects in scalar-tensor theories of gravity

Scalar-tensor theory predicts solutions to the gravitational field equations which describe compact objects in the presence of a non-minimally coupled scalar field to the Einstein tensor. These objects are black holes with scalar hair and wormholes supporting scalar phantom matter. The evolution of test fields in fixed asymptotically-flat backgrounds of exotic compact objects leads to the formation of echoes in the ringdown signal, which designate the existence of trapping regions close to the event horizon. Here, we consider minimally-coupled test scalar fields propagating on compact object solutions of the Horndeski action, which possess an effective cosmological constant, leading to anti-de Sitter asymptotics, and show that echoes can form in the ringdown waveform due to the entrapment of test fields between the photon sphere and the effective asymptotic boundary. Although the presence of an event horizon leads to the usual echoes with decaying amplitude, signifying modal stability of the scalarized black hole considered, we find that test scalar fields propagating on a scalarized wormhole solution give rise to echoes of constant and equal amplitude to that of the initial ringdown, indicating the existence of normal modes. Finally, we find that, near extremality, the test field exhibits a concatenation of echoes; the primary ones are associated with the trapping region between the photon sphere and the effective anti-de Sitter boundary while the secondary ones are linked to the existence of a potential well at the throat of the wormhole.

What does a quantum black hole look like?

We consider a free theory of multiple scalar fields at finite temperature and study the induced geometry defined through a free flow of the scalar fields, following the method proposed by the present authors as a possible candidate of the constructive approach for AdS/CFT correspondence. We find that the holographic metric has the following properties: i) It is an asymptotic Anti-de Sitter (AdS) black brane metric with some unknown matter contribution. ii) It has no coordinate singularity and milder curvature singularity. iii) Its time component decays exponentially at a certain AdS radial slice. We find that the matter spreads all over the space, which we speculate to be due to thermal excitation of infinitely many massless higher spin fields. We conjecture that the above three are generic features of a black hole holographically realized by the flow equation method.

Massive particles in the Einstein–Lovelock–anti-de Sitter black hole spacetime

An interpretation to the physics of stable geodesics of massive particles in black hole backgrounds has been recently proposed in the context of the AdS/CFT correspondence. It was argued that the existence of stable orbits indicates that the dual state does not thermalize on a thermal time scale and the bulk excitations can be interpreted as metastable states in the dual field theory. Here we study motion of massive particles in the background of the D-dimensional asymptotically anti-de Sitter (AdS) black holes in the Einstein–Lovelock theory. We show that, unlike the asymptotically flat case, for any kind of higher curvature Lovelock corrections there appear a stable circular orbit at a distance from the black hole. We find the general analytical expressions for the frequencies of distant circular orbits and radial oscillation frequencies. We show that the corresponding correction has the same power as in the Schwarzschild–AdS case, implying a universal scaling with the temperature for any Lovelock theory.

Lessons for quantum cosmology from anti–de Sitter black holes

Gravitational physics is arguably better understood in the presence of a negative cosmological constant than a positive one, yet there exist strong technical similarities between the two settings. These similarities can be exploited to enhance our understanding of the more speculative realm of quantum cosmology, building on robust results regarding anti-de Sitter black holes describing the thermodynamics of holographic quantum field theories. To this end, we study 4-dimensional gravitational path integrals in the presence of a negative cosmological constant, and with minisuperspace metrics. We put a special emphasis on boundary conditions and integration contours. The Hawking-Page transition is recovered and we find that below the minimum temperature required for the existence of black holes the corresponding saddle points become complex. When the asymptotic anti-de Sitter space is cut off at a finite distance, additional saddle points contribute to the partition function, albeit in a very suppressed manner. These findings have direct consequences for the no-boundary proposal in cosmology, because the anti-de Sitter calculation can be brought into one-to-one correspondence with a path integral for de Sitter space with Neumann conditions imposed at the nucleation of the universe. Our results lend support to recent implementations of the no-boundary proposal focusing on momentum conditions at the "big bang".

Flat-space limit of extremal curves

According to the Ryu-Takayanagi prescription, the entanglement entropy of subsystems in the boundary conformal field theory (CFT) is proportional to the area of extremal surfaces in bulk asymptotically Anti-de Sitter (AdS) spacetimes. The flat-space limit of these surfaces is not well defined in the generic case. We introduce a new curve in the three-dimensional asymptotically AdS spacetimes with a well-defined flat-space limit. We find this curve by using a new vector, which is vanishing on it and is normal to the bulk modular flow of the original interval in the two-dimensional CFT. The flat-space limit of this new vector is well defined and gives rise to the bulk modular flow of the corresponding asymptotically flat spacetime. Moreover, after Rindler transformation, this new vector is the normal Killing vector of the BTZ inner horizon. We reproduce all known results about the holographic entanglement entropy of Bondi-Metzner-Sachs invariant field theories, which are dual to the asymptotically flat spacetimes.

A new formula for conserved charges of Lovelock gravity in AdS space–times and its generalization

Within the framework of the Lovelock gravity theory, we propose a new rank-four divergenceless tensor consisting of the Riemann curvature tensor and inheriting its algebraic symmetry characters. Such a tensor can be adopted to define conserved charges of the Lovelock gravity theory in asymptotically anti-de Sitter (AdS) space–times. Besides, inspired with the case of the Lovelock gravity, we put forward another general fourth-rank tensor in the context of an arbitrary diffeomorphism invariant theory of gravity described by the Lagrangian constructed out of the curvature tensor. On basis of the newly-constructed tensor, we further suggest a Komar-like formula for the conserved charges of this generic gravity theory.

The rotating black hole interior: Insights from gravitational collapse in AdS3 spacetime

We present results from a numerical study of rotating black hole formation in 3-dimensional asymptotically anti-de Sitter (AdS) spacetime, focusing on the structure of the black hole interior. While black holes in $AdS_3$ are of theoretical interest for a wide variety of reasons, we choose to study this system primarily as a toy model for astrophysical (4-dimensional) black holes formed from gravitational collapse. We investigate the effect of angular momentum on the geometry inside the event horizon, and see qualitative changes in the interior structure as a function of the spin parameter. For low spins, we find that a central spacelike curvature singularity forms, connecting to a singular, null Cauchy horizon. For spins above a threshold consistent with the linear analysis of Dias, Reall and Santos, curvature on the Cauchy horizon remains bounded, signaling a violation of the strong cosmic censorship conjecture. Further increasing the spin leads to a decrease in the relative size of the spacelike branch of the singularity, which vanishes completely above a second threshold. In these high-spin cases, the interior evolution is bounded by a regular Cauchy horizon, which extends all the way inward to a regular, timelike origin. We further explore the geodesic focusing ("gravitational shock-wave") effect predicted to occur along the outgoing branch of the inner horizon, first described by Marolf and Ori. Remarkably, we observe the effect at late times in all of the black holes we form, even those in which the inner apparent horizon collapses to zero radius early in their evolution.

Generalized geometrical coupling for vector field localization on thick brane in asymptotic anti–de Sitter spacetime

It is known that a five-dimensional free vector field ${A}_{M}$ cannot be localized on Randall-Sundrum (RS)-like thick branes---namely, the thick branes embedded in asymptotic anti--de Sitter spacetime. To localize a vector field on the RS-like thick brane, an extra coupling term should be introduced. We generalize the geometrical coupling mechanism by adding two mass terms ($\ensuremath{\alpha}R{g}^{MN}{A}_{M}{A}_{N}+\ensuremath{\beta}{R}^{MN}{A}_{M}{A}_{N}$) to the action. We decompose the fundamental vector field ${A}_{M}$ into three parts: transverse vector part ${\stackrel{^}{A}}_{\ensuremath{\mu}}$ and scalar parts $\ensuremath{\phi}$ and ${A}_{5}$. Then we find that the transverse vector part ${\stackrel{^}{A}}_{\ensuremath{\mu}}$ decouples from the scalar parts. To eliminate the tachyonic modes of ${\stackrel{^}{A}}_{\ensuremath{\mu}}$, the two coupling parameters $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ should satisfy a relation. Combining the restricted condition, we can get a combination parameter as $\ensuremath{\gamma}=\frac{3}{2}\ifmmode\pm\else\textpm\fi{}\sqrt{1+12\ensuremath{\alpha}}$. Only if $\ensuremath{\gamma}>1/2$ can the zero mode of ${\stackrel{^}{A}}_{\ensuremath{\mu}}$ be localized on the RS-like thick brane. We also investigate the resonant character of the vector part ${\stackrel{^}{A}}_{\ensuremath{\mu}}$ for a general RS-like thick brane with a warp factor $A(z)=\ensuremath{-}\mathrm{ln}(1+{k}^{2}{z}^{2})/2$ by choosing the relative probability method. The results show that the massive resonant Kaluza-Klein modes can exist only for $\ensuremath{\gamma}>3$. The number of resonant Kaluza-Klein states increases with the combination parameter $\ensuremath{\gamma}$, and the lifetime of the first resonant state can be as long as our Universe's. This indicates that the vector resonances might be considered one of the candidates of dark matter. Combining the conditions of experimental observations, the constraint shows that the parameter $k$ has a lower limit with $k\ensuremath{\gtrsim}{10}^{\ensuremath{-}17}\text{ }\text{ }\mathrm{eV}$, the combination parameter $\ensuremath{\gamma}$ should be greater than 57, and, accordingly, the mass of the first resonant state should satisfy ${m}_{1}\ensuremath{\gtrsim}{10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{eV}$.

Phase structures and transitions of Born\u2013Infeld black holes in a grand canonical ensemble

To make a Born–Infeld (BI) black hole thermally stable, we consider two types of boundary conditions, i.e., the asymptotically anti-de Sitter (AdS) space and a Dirichlet wall placed in the asymptotically flat space. The phase structures and transitions of these two types of BI black holes, namely BI-AdS black holes and BI black holes in a cavity, are investigated in a grand canonical ensemble, where the temperature and the potential are fixed. For BI-AdS black holes, the globally stable phases can be the thermal AdS space. For small values of the potential, there is a Hawking-Page-like first order phase transition between the BI-AdS black holes and the thermal-AdS space. However, the phase transition becomes zeroth order when the values of the potential are large enough. For BI black holes in a cavity, the globally stable phases can be a naked singularity or an extremal black hole with the horizon merging with the wall, which both are on the boundaries of the physical parameter region. The thermal flat space is never globally preferred. Besides a first order phase transition, there is a second order phase transition between the globally stable phases. Thus, it shows that the phase structures and transitions of BI black holes with these two different boundary conditions have several dissimilarities.