Asymptotically Anti-de Sitter Spacetimes Research Articles

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.

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.

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.

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.

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.

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 ${m}_{1}\ensuremath{\gtrsim}{10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{eV}$.

Quasinormal Modes of the Planar Black Holes of a Particular Lovelock Theory**Supported by Brazilian funding agencies Fundaç ao de Amparo à Pesquisa do Estado de S ao Paulo (FAPESP), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenaç ao de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), and National Natural Science Foundation of China (NNSFC) under Grant No. 11805166

In this work, we study the scalar quasinormal modes of a planar black hole metric in asymptotic anti-de Sitter spacetime derived from a particular Lovelock theory. The quasinormal frequencies are evaluated by adopting the Horowitz-Hubeny method as well as a matrix formalism. Also, the temporal evolution of small perturbations is studied by using finite difference method. The roles of the dimension of the spacetime, the parameter of the metric k, as well as the temperature of the background black hole, are discussed. It is observed that the particular form of the metric leads to quasinormal frequencies whose real parts are numerically insignificant. The black hole metric is found to be stable against small scalar perturbations.

Nonequilibrium condensation process of a holographic p -wave superconductor

We study the nonequilibrium condensation process of a holographic $p$-wave superconductor model, which is described by Einstein-Maxwell theory coupled with the charged complex vector field in asymptotic anti-de Sitter (AdS) spacetime. By solving the gravitational dynamics in the asymptotic AdS spacetime numerically, we obtain the full time dependent solution of the system, and observe a dynamical process from the perturbed Reissner-Nordstr\om-AdS black hole to the anisotropic black hole with vector hair when the initial black hole temperature is smaller than the critical temperature ${T}_{c}$. By holography, this nonlinear dynamical process is then dual to the phase transition process from a normal state to a $p$-wave superconducting state on the boundary theory. We also investigate the time evolution of the superconducting condensate operator and horizon area.

Fixed mesh refinement in the characteristic formulation of general relativity

We implement a spatially fixed mesh refinement under spherical symmetry for the characteristic formulation of General Relativity. The Courant-Friedrich-Levy (CFL) condition lets us deploy an adaptive resolution in (retarded-like) time, even for the nonlinear regime. As test cases, we replicate the main features of the gravitational critical behavior and the spacetime structure at null infinity using the Bondi mass and the News function. Additionally, we obtain the global energy conservation for an extreme situation, i.e. in the threshold of the black hole formation. In principle, the calibrated code can be used in conjunction with an ADM 3+1 code to confirm the critical behavior recently reported in the gravitational collapse of a massless scalar field in an asymptotic anti-de Sitter spacetime. For the scenarios studied, the fixed mesh refinement offers improved runtime and results comparable to code without mesh refinement.

Gravitational geons in asymptotically anti-de Sitter spacetimes

We report on numerical constructions of fully non-linear geons in asymptotically anti-de Sitter (AdS) spacetimes in four dimensions. Our approach is based on 3  +  1 formalism and spectral methods in a gauge combining maximal slicing and spatial harmonic coordinates. We are able to construct several families of geons seeded by different families of spherical harmonics. We can reach unprecedentedly high amplitudes, with mass of order  ∼1/2 of the AdS length, and with deviations of the order of 50% compared to third order perturbative approaches. The consistency of our results with numerical resolution is carefully checked and we give extensive precision monitoring techniques. All global quantities, such as mass and angular momentum, are computed using two independent frameworks that agree with each other at the 0.1% level. We also provide strong evidence for the existence of ‘excited’ (i.e. with one radial node) geon solutions of Einstein equations in asymptotically AdS spacetimes by constructing them numerically.

Eikonal instability of Gauss-Bonnet–(anti-)–de Sitter black holes

Here we have shown that asymptotically anti-de Sitter (AdS) black holes in the Einstein-Gauss-Bonnet (GB) theory are unstable under linear perturbations of spacetime in some region of parameters. This (eikonal) instability develops at high multipole numbers. We found the exact parametric regions of the eikonal instability and extended this consideration to asymptotically flat and de Sitter cases. The approach to the threshold of instability is driven by purely imaginary quasinormal modes, which are similar to those found recently in [5] for the higher curvature corrected black hole with the planar horizon. The found instability may indicate limits of holographic applicability of the GB-AdS backgrounds. Recently, through the analysis of critical behavior in AdS space-time in the presence of Gauss-Bonnet term, it was shown [19] that that, if the total energy content of the AdS space-time is small, then no black holes can be formed with mass less than some critical value. A similar mass gap was also found when considering collapse of mass shells in asymptotically flat Gauss-Bonnet theories [20]. The found instability of all sufficiently small Einstein-Gauss-Bonnet-AdS, -dS and asymptotically flat black holes may explain the existing mass gaps in their formation.

Black holes in anti–de Sitter spacetime: Quasinormal modes, tails, and flat spacetime

Black holes in asymptotically anti-de Sitter (AdS) spacetimes have been the subject of intense scrutiny, including detailed frequency-domain analysis and full nonlinear evolutions. Remarkably, studies of linearized perturbations in the time-domain are scarce or non-existing. We close this gap by evolving linearized scalar wavepackets in the background of rotating BHs in AdS spacetimes. Our results show a number of interesting features. Small BHs in AdS behave as asymptotically flat BHs for early/intermediate times, displaying the same ringdown modes and power-law tails. As the field bounces back and forth between the horizon and the timelike boundary it "thermalizes" and the modes of AdS settle in. Finally, we have indications that wavepackets in the vicinity of fastly spinning BHs grow exponentially in time, signalling a superradiant instability of the geometry previously reported through a frequency-domain analysis.

Action principles for Transgression and Chern-Simons AdS gravities

Chern-Simons gravities are theories with a lagrangian given by a Chern-Simons form constructed from a space-time gauge group. In previous investigations we showed that, for some special field configurations that are solutions of the field equations, the extension from Chern-Simons to Transgression forms as lagrangians, motivated by gauge invariance, automatically yields the boundary terms required to regularize the theory, giving finite conserved charges and black hole thermodynamics. Further work by other researchers showed that one of the action functionals considered in the above mentioned work yields a well defined action principle in the metric (zero torsion) case and for asymptotically Anti de Sitter (AdS) space-times. In the present work we consider several action functionals for Chern-Simons AdS gravity constructed from Transgression forms, and show the action principles to be well defined and the Noether charges and Euclidean action to be finite for field configurations satisfying only that the gauge field curvature (field strength) for the AdS gauge group is asymptotically finite. For that purpose we consider an asymptotic expansion of the vielbein and spin connection that may be regarded as a perturbation of an AdS space-time, but allowing a non zero torsion. Our results are of potential interest for Lovelock gravity theories, as it has been shown that the boundary terms dictated by the transgressions for Chern-Simons gravities are also suitable to regularize Lovelock theories.

What drives AdS spacetime unstable?

We calculate the spectrum of linear perturbations of standing wave solutions discussed in [Phys. Rev. D 87, 123006 (2013)] as the first step of investigating the stability of the globally regular, asymptotically anti--de Sitter (AdS), time-periodic solutions discovered in [Phys. Rev. Lett. 111, 051102 (2013)]. We show that while this spectrum is only asymptotically nondispersive (as contrasted with the pure AdS case), putting a small standing wave solution on top of an AdS solution indeed prevents the turbulent instability. Thus we support the idea advocated in previous works that the nondispersive character of the spectrum of linear perturbations of AdS space is crucial for the conjectured turbulent instability.

Flowing along the edge: Spinning up black holes in AdS spacetimes with test particles

We investigate the consequences of throwing point particles into odd-dimensional Myers-Perry black holes in asymptotically anti-de Sitter (AdS) backgrounds. We restrict our attention to the case in which the angular momenta of the background geometry are all equal. This process allows us to test the generalization of the weak cosmic censorship conjecture to asymptotically AdS spacetimes in higher dimensions. We find no evidence for overspinning in D = 5, 7, 9 and 11 dimensions. Instead, test particles carrying the maximum possible angular momentum that still fall into an extremal rotating black hole generate a flow along the curve of extremal solutions.

Lifshitz holographic renormalization from anti-de Sitter

Lifshitz space–times with critical exponent z = 2 can be obtained by dimensional reduction of Schrödinger space–times with critical exponent z = 0. The latter space–times are asymptotically anti-de Sitter (AdS) solutions of AdS gravity coupled to an axion–dilaton system (or even just a massless scalar field). This basic observation is used to perform holographic renormalization for four-dimensional asymptotically locally Lifshitz space–times by dimensional reduction of the corresponding problem of holographic renormalization for five-dimensional asymptotically AdS space–times coupled to an axion–dilaton system. In this setup the four-dimensional structure of the Lifshitz – Fefferman-Graham expansion and the structure of the counterterm action, including the scale anomaly, will be summarized.

Singularities in asymptotically anti–de Sitter spacetimes

We consider singularity theorems in asymptotically anti-de Sitter (AdS) spacetimes. In the first part, we discuss the global methods used to show geodesic incompleteness and see that when the conditions imposed in Hawking and Penrose's singularity theorem are satisfied, a singularity must appear in asymptotically AdS spacetime. The recent observations of turbulent instability of asymptotically AdS spacetimes indicate that AdS spacetimes are generically singular even if a closed trapped surface, which is one of the main conditions of the Hawking and Penrose theorem, does not exist in the initial hypersurface. This may lead one to expect to obtain a singularity theorem without imposing the existence of a trapped set in asymptotically AdS spacetimes. This, however, does not appear to be the case. We consider, within the use of global methods, two such attempts and discuss difficulties in eliminating conditions concerning a trapped set from singularity theorems in asymptotically AdS spacetimes. Then in the second part, we restrict our attention to the specific case of spherically symmetric, perfect fluid systems in asymptotically AdS spacetime, and show that under a certain condition concerning dynamics of the fluid, a closed trapped surface must form, and as a combined result with Hawking and Penrose's theorem, that such a spacetime must be singular.

QUANTUM STATES OF THE SPACETIME, AND FORMATION OF BLACK HOLES IN AdS

We argue that a nonperturbative description of quantum gravity should involve two (noninteracting) copies of a dual field theory on the boundary, and describe the states of the spacetimes accordingly. So, for instance, a complete description of the asymptotically Anti-de-Sitter (AdS) spacetimes is given by two copies of the conformal field theory (CFT) associated to the global AdS spacetime. We also argue that, in this context, gravitational collapse and formation of a black hole may be described by unitary evolution of the dual nonperturbative degrees of freedom.