We propose a definition of asymptotically plane wave spacetimes in vacuum gravity in terms of the asymptotic falloff of the metric, and discuss the relation to previously constructed exact solutions. We construct a well-behaved action principle for such spacetimes, using the formalism developed by Mann and Marolf. We show that this action is finite on-shell and that the variational principle is well-defined for solutions of vacuum gravity satisfying our asymptotically plane wave falloff conditions.
In this paper, we investigate the global monopole in asymptotically dS/Ads spacetime and find that the mass of the monopole in the asymptotically dS spacetime could be positive if the cosmological constant is greater than a critical value. This shows that the gravitational field of the global monopole could be attractive or repulsive depending on the value of the cosmological constant.
The divergences of the gravitational action are analyzed for spacetimes that are asymptotically anti-de Sitter and asymptotically flat. The gravitational action is rendered finite using a local counterterm prescription, and the relation of this method to the traditional reference spacetime is discussed. For AdS, an iterative procedure is devised that determines the counterterms efficiently. For asymptotically flat space, we use a different method to derive counterterms which are sufficient to remove divergences in most cases.
We consider in more detail the covariant counterterm proposed by Mann and Marolf in asymptotically flat spacetimes. With an eye to specific practical computations using this counterterm, we present explicit expressions in general $d$ dimensions that can be used in the so-called `cylindrical cut-off' to compute the action and the associated conserved quantities for an asymptotically flat spacetime. As applications, we show how to compute the action and the conserved quantities for the NUT-charged spacetime and for the Kerr black hole in four dimensions.
We report that a class of three-dimensional bimetric theories contain asymptotically flat solutions. These spacetimes can be cast in a set of asymptotic conditions at null infinity which are preserved under the infinite dimensional BMS group. Moreover, the algebra of the canonical generators exhibits a central extension. The possibility that these solutions describe regular black holes is also discussed.
Under a Scherk-Schwarz compactification, the AdS soliton and black brane provide a dual description to a confinement/deconfinement phase transition. We extend this construction to asymptotically Lifshitz spacetimes. In particular, we show that there must be a phase transition between the soliton and black hole if the solutions exist. We also construct these solutions numerically and compute the phase diagram.
We present a cylindrically symmetric, Petrov type D, nonexpanding, shear free and vorticity free solution of Einstein's field equations. The spacetime is asymptotically flat radially and regular everywhere except on the symmetry axis where it possesses a naked curvature singularity. The energy momentum tensor of the spacetime is that for an anisotropic fluid which satisfies the different energy conditions. This spacetime is used to generate a rotating spacetime which admits closed timelike curves and may represent a Cosmic Time Machine.
We numerically investigate the stability of four-dimensional asymptotically anti-de Sitter ($AdS_4$) spacetime for a class of nonminimally coupled scalar field theories. In particular, we study how the coupling affects the formation of black holes and transfer of energy to different spatial/temporal scales. We conclude by detailing the well-known analogy between the nonminimally coupled scalar-field stress-energy tensor and that of a viscous relativistic fluid, and discuss the limitations of that analogy when it is applied to anisotropic scalar field configurations in asymptotically $AdS$ spac…
We prove that certain asymptotically flat initial data sets with nontrivial topology and/or differentiable structure collapse to form singularities. The class of such initial data sets is characterized by a new smooth invariant, the maximal Yamabe invariant, defined through smooth compactification of the asymptotically flat manifold. Our singularity theorem applies to spacetimes admitting a Cauchy surface of nonpositive maximal Yamabe invariant with initial data that satisfies the dominant energy condition. This class of spacetimes includes simply connected spacetimes with a single asymptotic …
In order to get a better understanding of holographic properties of gravitational theories with a vanishing cosmological constant, we analyze in detail the relation between asymptotically anti-de Sitter and asymptotically flat spacetimes in three dimensions. This relation is somewhat subtle because the limit of vanishing cosmological constant cannot be naively taken in standard Fefferman-Graham coordinates. After reformulating the standard anti-de Sitter results in Robinson-Trautman coordinates, a suitably modified Penrose limit is shown to connect both asymptotic regimes.
We follow the spirit of a recent proposal to show that previous computations for asymptotically flat spacetimes in four dimensions at null infinity can be re-interpreted in terms of a well-defined holographic current algebra for the time component of the currents. The analysis is completed by the current algebra for the spatial components.
Unlike the extremal Reissner - Nordström black hole in ordinary spacetime, the one in anti-de Sitter spacetime is a minimum of action and has zero entropy if quantization is carried out after extremalization. However, if extremalization is carried out after quantization, then the entropy is a quarter of the area as in the usual case.
We numerically simulate gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative cosmological constant in five spacetime dimensions and obtain a family of non-spherically symmetric solutions, including those that form two distinct black holes on the axis. We find that these configurations collapse faster than spherically symmetric ones of the same mass and radial compactness. Similarly, they require less mass to collapse within a fixed time…
We study several properties of some new charges of asymptotically flat spacetimes. These dual supertranslation charges are akin to the magnetic large $U(1)$ charges in QED. In this paper we find the symmetries associated with these charges and show that the global dual supertranslation charge is topological because it is invariant under globally defined, smooth variations of the asymptotic metric. We also exhibit spacetimes where the charge does not vanish and we find dynamical processes that interpolate between regions with different values of these charges.
We derive exact magnetically charged, static and spherically symmetric black hole solutions of the four-dimensional Einstein-Born-Infeld-dilaton gravity. These solutions are neither asymptotically flat nor (anti)-de Sitter. The properties of the solutions are discussed. It is shown that the black holes are stable against linear radial perturbations.
We construct the phase space of 3-dimensional asymptotically flat spacetimes that forms the bulk metric representation of the BMS group consisting of both supertranslations and superrotations. The asymptotic symmetry group is a unique copy of the BMS group at both null infinities and spatial infinity. The BMS phase space obeys a notion of holographic causality and can be parametrized by boundary null fields. This automatically leads to the antipodal identification of bulk fields between past and future null infinity in the absence of a global conical defect.
We use geodesic probes to recover the entire bulk metric in certain asymptotically AdS spacetimes. Given a spectrum of null geodesic endpoints on the boundary, we describe two remarkably simple methods for recovering the bulk information. After examining the issues which affect their application in practice, we highlight a significant advantage one has over the other from a computational point of view, and give some illustrative examples. We go on to consider spacetimes where the methods cannot be used to recover the complete bulk metric, and demonstrate how much information can be recovered i…
We prove uniqueness, existence, and regularity results for maximal hypersurfaces in spacetimes with a conformal completion at timelike infinity and asymptotically constant scalar curvature, as relevant for asymptotically AdS spacetimes. This work is dedicated to Yvonne Choquet-Bruhat on the occasion of her upcoming 99th birthday.
We study the propagation of a massless scalar wave in de Sitter spacetime perturbed by an arbitrary central mass. By focusing on the late time limit, this probes the portion of the scalar signal traveling inside the null cone. Unlike in asymptotically flat spacetimes, the amplitude of the scalar field detected by an observer at timelike infinity does not decay back to zero but develops a spacetime constant shift - both at zeroth and first order in the central mass M. This indicates that massless scalar field propagation in asymptotically de Sitter spacetimes exhibits both linear and nonlinear …
We generalize a notion of 'conserved' charges given by Wald and Zoupas to the asymptotically de Sitter spacetimes. Surprisingly, our construction is less ambiguous than the one encountered in the asymptotically flat context. An expansion around exact solutions possessing Killing vectors provides their physical meaning. In particular, we discuss a question of how to define energy and angular momenta of gravitational waves propagating on Kottler and Carter backgrounds. We show that obtained expressions have a correct limit as $Λ\to 0$. We also comment on the relation between this approach and th…
We consider $n$-dimensional asymptotically anti-de Sitter spacetimes in higher curvature gravitational theories with $n \geq 4$, by employing the conformal completion technique. We first argue that a condition on the Ricci tensor should be supplemented to define an asymptotically anti-de Sitter spacetime in higher curvature gravitational theories and propose an alternative definition of an asymptotically anti-de Sitter spacetime. Based on that definition, we then derive a conservation law of the gravitational field and construct conserved quantities in two classes of higher curvature gravitati…
A rotating thin shell in a (2+1)-dimensional asymptotically AdS spacetime is studied. The spacetime exterior to the shell is the rotating BTZ spacetime and the interior is the empty spacetime with a cosmological constant. Through the Einstein equation in (2+1)-dimensions and the corresponding junction conditions we calculate the dynamical relevant quantities, namely, the rest energy-density, the pressure, and the angular momentum flux density. We also analyze the matter in a frame where its energy-momentum tensor has a perfect fluid form. In addition, we show that Machian effects, such as the …
We discuss a phase transition of a Reissner-Nordström black hole to a hairy black hole in asymptotically flat spacetime. The hair is due to a massive charged scalar field. The no-hair theorem is evaded thanks to a derivative coupling of the scalar field to the Einstein tensor. The resulting hairy configuration is spherically symmetric. We solve the equations analytically near the transition temperature and show that the hair is concentrated near the horizon decaying exponentially away from it.
We examine general features of causal wedges in asymptotically AdS spacetimes and show that in a wide variety of cases they have non-trivial topology. We also prove some general results regarding minimal area surfaces on the causal wedge boundary and thereby derive constraints on the causal holographic information. We go on to demonstrate that certain properties of the causal wedge impact significantly on features of extremal surfaces which are relevant for computation of holographic entanglement entropy.
Horava gravity theory possesses global Lifshitz space as a solution and has been conjectured to provide a natural framework for Lifshitz holography. We derive the conditions on the two derivative Horava gravity Lagrangian that are necessary for static, asymptotically Lifshitz spacetimes with flat transverse dimensions to contain a universal horizon, which plays a similar thermodynamic role as the Killing horizon in general relativity. Specializing to z=2 in 1+2 dimensions, we then numerically construct such regular solutions over the whole spacetime. We calculate the mass for these solutions a…
Using Killing-Yano symmetries, we construct conserved charges of spacetimes that asymptotically approach to the flat or Anti-de Sitter spaces only in certain directions. In D dimensions, this allows one to define gravitational charges (such as mass and angular momenta densities) of p-dimensional branes/solitons or any other extended objects that curve the transverse space into an asymptotically flat or AdS one. Our construction answers the question of what kind of charges the antisymmetric Killing-Yano tensors lead to.
It is argued that the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions should be taken as the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a consequence, two dimensional conformal field theory techniques will play as fundamental a role in this context of direct physical interest as they do in three dimensional anti-de Sitter gravity.
We investigate black brane solutions in asymptotically Lifshitz spacetime in 3+1-dimensional Horndeski gravity, which admit a critical exponent fixed at $z=1/2$. The cosmological constant depends on $z$ as $Λ=-(1+2z)/L^{2}$. We compute the shear viscosity in the 2+1-dimensional dual boundary field theory via holographic correspondence. We investigate the violation of the bound for viscosity to entropy density ratio of $η/s\geq1/(4π)$ at $z=1/2$.
We present a modified version of the boundary counterterm method for removing divergences from the action of an asymptotically $AdS$ spacetime. The standard approach renders the action finite but leaves diffeomorphism invariance partially broken if the dimension of the spacetime is odd. We show that this symmetry is restored by a new boundary counterterm, needed to cancel a divergence that appears in dimensional regularization. The result is a finite, diffeomorphism invariant action appropriate for gravitational physics. As an example we calculate the action for the Kerr-$AdS_5$ black hole. Un…
We present a class of black string spacetimes which asymptote to maximally symmetric plane wave geometries. Our construction will rely on a solution generating technique, the null Melvin twist, which deforms an asymptotically flat black string spacetime to an asymptotically plane wave black string spacetime while preserving the event horizon.
In an attempt to study asymptotically plane wave spacetimes which admit an event horizon, we find solutions to vacuum Einstein's equations in arbitrary dimension which have a globally null Killing field and rotational symmetry. We show that while such solutions can be deformed to include ones which are asymptotically plane wave, they do not posses a regular event horizon. If we allow for additional matter, such as in supergravity theories, we show that it is possible to have extremal solutions with globally null Killing field, a regular horizon, and which, in addition, are asymptotically plane…
We analyze asymptotic properties of higher-dimensional vacuum spacetimes admitting a "non-degenerate" geodetic multiple WAND. After imposing a fall-off condition necessary for asymptotic flatness, we determine the behaviour of the Weyl tensor as null infinity is approached along the WAND. This demonstrates that these spacetimes do not "peel-off" and do not contain gravitational radiation (in contrast to their four-dimensional counterparts). In the non-twisting case, the uniqueness of the Schwarzschild-Tangherlini metric is also proven.
As an extension of arXiv:\{2002.02448, 2008.10740\} we present a physical protocol that a set of observers can use to detect a pure state in the bulk when they are spread across a small cut near $\mathcal{I}^+_-$ in flat spacetime. The protocol involves the modification of a bulk state using simple unitary operators and measurements of the energy of the state. The states that we study are constructed by acting with low energy operators on a vacuum state such that a perturbative analysis is valid. We restrict ourselves to $3+1$ dimensional spacetimes and only consider massless excitations. From…
We give a definition of asymptotically locally Lifshitz spacetimes, with boundary data appropriate for a non-relativistic theory on the boundary. Solutions satisfying these boundary conditions are constructed in an asymptotic expansion. We identify the boundary data with sources for dual field theory operators, and give a prescription for calculating the one-point functions of the field theory operators (including the stress tensor) in the presence of arbitrary sources. The divergences in these one-point functions can be cancelled by holographic renormalization, adding counterterms which are l…
We classify the asymptotic charges of a class of polyhomogeneous asymptotically-flat spacetimes with finite shear, generalising recent results on smooth asymptotically-flat spacetimes. Polyhomogenous spacetimes are a formally consistent class of spacetimes that do not satisfy the well-known peeling property. As such, they constitute a more physical class of asymptotically-flat spacetimes compared to the smooth class. In particular, we establish that the generalised conserved non-linear Newman-Penrose charges that are known to exist for such spacetimes are a subset of asymptotic BMS charges.
In this paper, we investigate a $6$-dimensional smooth thick braneworld model which contains a compact extra dimension and an infinite large one. The braneworld is generated by a real scalar field with a $ϕ^6$ potential and the bulk is asymptotically $\text{AdS}_6$ spacetime. The geometry achieves the localization of the free $U(1)$ gauge field, which is a problem in the $5$-dimensional Randall-Sundrum-like models. In addition, we analyze the stability of the braneworld system and the localization of gravitons.
The possibility that the asymptotic quasi-normal mode (QNM) frequencies can be used to obtain the Bekenstein-Hawking entropy for the Schwarzschild black hole -- commonly referred to as Hod's conjecture -- has received considerable attention. To test this conjecture, using monodromy technique, attempts have been made to analytically compute the asymptotic frequencies for a large class of black hole spacetimes. In an earlier work, two of the current authors computed the high frequency QNMs for scalar perturbations of $(D+2)$ dimensional spherically symmetric, asymptotically flat, single horizon …
We provide a prescription to compute the gravitational multipole moments of compact objects for asymptotically de Sitter spacetimes. Our prescription builds upon a recent definition of the gravitational multipole moments in terms of Noether charges associated to specific vector fields, within the residual harmonic gauge, dubbed multipole symmetries. We first derive the multipole symmetries for spacetimes which are asymptotically de Sitter; we also show that these symmetry vector fields eliminate the non-propagating degrees of freedom from the linearized gravitational wave equation in a suitabl…
In this work, we present a numerical scheme to study the quasinormal modes of the time-dependent Vaidya black hole metric in asymptotically anti-de Sitter spacetime. The proposed algorithm is primarily based on a generalized matrix method for quasinormal modes. The main feature of the present approach is that the quasinormal frequency, as a function of time, is obtained by a generalized secular equation and therefore a satisfactory degree of precision is achieved. The implications of the results are discussed.
A consistent set of asymptotic conditions for higher spin gravity in three dimensions is proposed in the case of vanishing cosmological constant. The asymptotic symmetries are found to be spanned by a higher spin extension of the BMS3 algebra with an appropriate central extension. It is also shown that our results can be recovered from the ones recently found for asymptotically AdS3 spacetimes by virtue of a suitable gauge choice that allows to perform the vanishing cosmological constant limit.
Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective dimensionality of 2. The original argument leading to this result was based upon the anomalous dimension of Newton's constant. In the present paper we demonstrate that also the spectral dimension equals 2 microscopically, while it is equal to 4 on macroscopic scales. This result is an exact consequence of asymptotic safety and does not rely on any truncation. C…
A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics, convenient exploitation of the residual diffeomorphism freedom, and use of spectral methods for discretizing and solving the resulting differential equations. Relevant issues and choices leading to this approach are discussed in detail. Three examples, motivated by applications to non-equilibrium dynamics in strongly coupled gauge theories, are discussed as instructi…
Recent work has shown that the addition of an appropriate covariant boundary term to the gravitational action yields a well-defined variational principle for asymptotically flat spacetimes and thus leads to a natural definition of conserved quantities at spatial infinity. Here we connect such results to other formalisms by showing explicitly i) that for spacetime dimension $d \ge 4$ the canonical form of the above-mentioned covariant action is precisely the ADM action, with the familiar ADM boundary terms and ii) that for $d=4$ the conserved quantities defined by counter-term methods agree pre…
We attempt to understand the CFT$_1$ structure underlying (2+1)D gravity in flat spacetime via dimensional reduction. We observe that under superrotation, the hyperbolic (and dS$_2$) slices of flat spacetime transform to asymptotically (A)dS$_2$ slices. We consider a wedge region bounded by two such surfaces as End-of-the-World branes and employ Wedge holography to perform holographic reduction. We show that once we consider fluctuating branes, the localised theory on the branes is Jackiw-Teitelboim (JT) theory. Finally, using the dual description of JT, we derive an 1D Schwarzian theory at th…
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 rad…
Using holography, we study the collision of planar shock waves in strongly coupled N=4 supersymmetric Yang-Mills theory. This requires the numerical solution of a dual gravitational initial value problem in asymptotically anti-de Sitter spacetime.
Analytical approximations for $< ϕ^2 >$ of a quantized scalar field in ultrastatic asymptotically flat spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling $ξ$ to the scalar curvature, and in a zero or nonzero temperature vacuum state. The expression for $< ϕ^2 >$ is divided into low- and high-frequency parts. The expansion for the high-frequency contribution to this quantity is obtained. This expansion is analogous to the DeWitt-Schwinger one. As an example, the low-frequency contribution to $< ϕ^2 >$ is calculated on the background of the …
The numerical study indicates that there exists a relation between the quasinormal modes and the Davies point for a black hole. In this paper, we analytically study this relation for the charged Reissner-Nordström black holes in asymptotically flat and dS spacetimes. In the eikonal limit, the angular velocity $Ω$ and the Lyapunov exponent $λ$ of the photon sphere, respectively, corresponding to the real and imaginary parts of the quasinormal modes are obtained from the null geodesics. Both in asymptotically flat and dS spacetimes, we observe the spiral-like shapes in the complex quasinormal mo…
We consider two BF formulations of the theory of gravity with a negative cosmological constant, of Plebanski and of MacDowell-Mansouri. Both give the standard Einstein equations in the bulk but differ in expressions of edge charges. We compute the asymptotic charges explicitly in both theories for AdS-Schwarzschild, AdS-Kerr, and AdS-Taub--NUT solutions. We find that while in the case of the Plebanski theory the charges are divergent, they are finite for MacDowell-Mansouri theory. Furthermore, we show that in the case of the arbitrary asymptotically AdS spacetimes, MacDowell--Mansouri asymptot…
We define an asymptotic symmetry algebra for three-dimensional Goedel spacetimes supported by a gauge field which turns out to be the semi-direct sum of the diffeomorphisms on the circle with two loop algebras. A class of fields admitting this asymptotic symmetry algebra and leading to well-defined conserved charges is found. The covariant Poisson bracket of the conserved charges is then shown to be centrally extended to the semi-direct sum of a Virasoro algebra and two affine algebras.
We explore the question of what happens with the asymptotically highly damped quasi-normal modes ($\ell$ fixed, $|ω_{I}|\to\infty$) when the underlying spacetime has no event horizons. We consider the characteristic oscillations of a scalar field in a large class of asymptotically flat spherically symmetric static spacetimes without (absolute) horizons, such that the class accommodates the cases that are known to be of some sort of physical interest. The question of the asymptotic quasi-normal modes in such spacetimes is relevant to elucidate the connection between the behavior of the asymptot…
Although gravitational actions diverge in asymptotically AdS spacetimes, boundary counterterms can be added in order to cancel out those divergences; such counterterms are known in general to third order in the Riemann tensor for the Einstein-Hilbert action. Considering foliations of AdS with an $S^m \times H^{d-m}$ boundary, we discuss a simple algorithm which we use to generate counterterms up to sixth order in the Riemann tensor, for the Einstein-Hilbert, Gauss-Bonnet and third-order-Lovelock Lagrangians. We also comment on other theories such as $F(R)$ gravity.
We revisit the asymptotically Anti de Sitter spacetimes in three dimensions. Using the conformal-completion technique, we formulate the boundary conditions in a covariant fashion and construct the global charges associated with the asymptotic symmetries. The charges so constructed are conserved for the asymptotic Killing vectors fields but are not conserved for the asymptotic conformal Killing vector fields. The quantity integrated to obtain the global charge is interpreted as the Brown-York boundary stress-energy tensor and it is found not to be traceless. The trace is interpreted as the trac…
We investigate static inhomogeneous charged planar black hole solutions of the Einstein-Maxwell system in an asymptotically anti-de Sitter spacetime. Within the framework of linear perturbations, the solutions are numerically and analytically constructed from the Reissner-Nordström-AdS black hole solution. The perturbation analysis predicts that the Cauchy horizon always disappears for any wavelength perturbation, supporting the strong cosmic censorship conjecture. For extremal black holes, we analytically show that an observer freely falling into the black hole feels infinite tidal force at t…
A numerical analysis shows that a class of scalar-tensor theories of gravity with a scalar field minimally and nonminimally coupled to the curvature allows static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. In the limit when the horizon radius of the black hole tends to zero, regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential $V(ϕ)$ of the theory is not positive semidefinite and such that its local minimum is also a zero of the potential, the scalar field settling asym…
We study a special two-dimensional dilaton gravity with Lagrangian $\mathcal{L}=\frac{1}{2}\sqrt{-g}(ϕR+{λ^2}{\rm sech}^2ϕ)$ where $λ$ is a parameter of dimension mass. This theory describes two-dimensional spacetimes that are asymptotically flat. Very interestingly, it has an exact solution for the metric, $\d s^2=-(c+\tanh λx)\d t^2+ \d x^2/(c+\tanh λ x)$, parametrized by $c$. For $c\in(-1,1)$, the solution presents an event horizon but no singularity. Because of the kink profile for the metric components appearing in the solution, we refer to the spacetime described by the metric as a {\it …
