The recent introduction of a boundary stress tensor for asymptotically flat spacetimes enabled a new construction of energy, momentum, and Lorentz charges. These charges are known to generate the asymptotic symmetries of the theory, but their explicit formulas are not identical to previous constructions in the literature. This paper corrects an earlier comparison with other approaches, including terms in the definition of the stress tensor charges that were previously overlooked. We show that these terms either vanish identically (for d > 4) or take a form that does not contribute to the conserved charges (for d=4). This verifies the earlier claim that boundary stress tensor methods for asymptotically flat spacetimes yield the same conserved charges as other approaches. We also derive some additional connections between the boundary stress tensor and the electric part of the Weyl tensor.
For spaces which are not asymptotically anti-de Sitter where the asymptotic behavior is deformed by replacing the cosmological constant by a dilaton scalar potential, we show that it is possible to have well-defined boundary stress-energy tensors and finite Euclidean actions by adding appropriate surface counterterms. We illustrate the method by the examples of domain-wall black holes in gauged supergravities, three-dimensional dilaton black holes and topological dilaton black holes in four dimensions. We calculate the boundary stress-energy tensor and Euclidean action of these black configura…
We study the conserved charges of supersymmetric solutions in the topologically massive gravity theory for both asymptotically flat and constant curvature geometries.
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.
Dilaton black hole solutions which are neither asymptotically flat nor (anti)-de Sitter but reduce to asymptotically flat solutions in some special limits have been known for a Liouville type dilatonic potential. It is shown how, by solving a pair of coupled differential equations, infinitesimally small angular momentum can be added to these static solutions to produce rotating black hole solutions.
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.
We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking the flat-space limit (zero cosmological constant limit) of new massive gravity. We propose that the dual field theory of the flat-space limit of new massive gravity can be described by a contracted conformal field theory which is invariant under the action of the BMS$_{3}$ group. Using the flat/contracted conformal field theory correspondence, we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. We check th…
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 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 compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern-Simons formulation for the Poincare group. The equivalent action is nothing but the Einstein-Hilbert term in the bulk plus half of the Gibbons-Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.
We show that the asymptotically flat hairy black holes, solutions of the Einstein field equations minimally coupled to a scalar field, previously discovered by one of us, present mode instability against linear radial perturbations. It is also shown that the number of unstable modes is finite and their frequencies can be made arbitrarily small.
We show that previously known non-asymptotically flat static black hole solutions of Einstein-Maxwell-dilaton theory may be obtained as near-horizon limits of asymptotically flat black holes. Specializing to the case of the dilaton coupling constant $α^2 = 3$, we generate from the non-asymptotically flat magnetostatic or electrostatic black holes two classes of rotating dyonic black hole solutions. The rotating dyonic black holes of the ``magnetic'' class are dimensional reductions of the five-dimensional Myers-Perry black holes relative to one of the azimuthal angles, while those of the ``ele…
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.
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 …
The general solution for the static, spherical and asymptotically flat braneworld is derived by solving the bulk Einstein equation and braneworld dynamics. We show that it involves a large arbitrariness, which reduces the predictability of the theory. Ways out of the difficulty are discussed.
In this paper, we are interested in a model of exact asymptotically flat charged hairy black holes in the background of dilaton potential. We study the weak gravitational lensing in the spacetime of hairy black hole in Einstein-Maxwell theory with a non-minimally coupled dilaton and its non-trivial potential. In doing so, we use the optical geometry of the flat charged hairy black hole for some range of parameter $γ$. For this purpose, by using Gauss-Bonnet theorem, we obtain the deflection angle of photon in a spherically symmetric and asymptotically flat spacetime. Moreover, we also investig…
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.
Starting from the Chern-Simons formulation, the two-dimensional dual theory for three-dimensional asymptotically flat Einstein gravity at null infinity is constructed. Solving the constraints together with suitable gauge fixing conditions gives in a first stage a chiral Wess-Zumino-Witten like model based on the Poincaré algebra in three dimensions. The next stage involves a Hamiltonian reduction to a BMS3 invariant Liouville theory. These results are connected to those originally derived in the anti-de Sitter case by rephrasing the latter in a suitable gauge before taking their flat-space lim…
The thermodynamics of three-dimensional asymptotically flat cosmological solutions that play the same role than the BTZ black holes in the anti-de Sitter case is derived and explained from holographic properties of flat space. It is shown to coincide with the flat-space limit of the thermodynamics of the inner black hole horizon on the one hand and the semi-classical approximation to the gravitational partition function associated to the entropy of the outer horizon on the other. This leads to the insight that it is the Massieu function that is universal in the sense that it can be computed at…
It was confirmed that the negative modes of the Euclidean section for asymptotically flat black holes reveal the thermodynamic instability of these black holes in the grand canonical ensemble (GCE). These include Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman black holes. In this work, we develop the relation between thermodynamic instability in the GCE and tachyonic instability for asymptotically flat black holes, where the latter is the onset for obtaining black holes with scalar hair. This implies that the tachyonic instability of black holes when introducing scalar coupling to th…
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 construct an infinite family of smooth asymptotically-flat supergravity solutions that have the same charges and angular momenta as general supersymmetric D1-D5-P black holes, but have no horizon. These solutions resemble the corresponding black hole to arbitrary accuracy outside of the horizon: they have asymptotically flat regions, AdS_3 x S^3 throats and very-near-horizon AdS_2 throats, which however end in a smooth cap rather than an event horizon. The angular momenta of the solutions are general, and in particular can take arbitrarily small values. Upon taking the AdS_3 x S^3 decouplin…
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 present a detailed analysis of the thermodynamics of exact asymptotically flat hairy black holes in Einstein-Maxwell-dilaton theory. We compute the regularized action, quasilocal stress tensor, and conserved charges by using a `counterterm method' similar to the one extensively used in the AdS-CFT duality. In the presence of a non-trivial dilaton potential that vanishes at the boundary we prove that, for some range of parameters, there exist thermodynamically stable black holes in the grand canonical and canonical ensembles. To the best of our knowledge, this is the first example of a therm…
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 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 construct finite mass, asymptotically flat black hole solutions in d=5 Einstein--Yang-Mills--Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordstrom solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations. In addition a solution in closed form describing an extremal black hole with non-Abelian hair is found for a special value of the Chern-Simons coupling constant.
We systematically derive the asymptotically flat five dimensional black rings in EMd gravity by using the sigma model structure of the dimensionally reduced field equations. New non-asymptotically flat EMd black ring solutions in five dimensions are also constructed and their physical properties are analyzed.
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 the interior of a recently constructed family of asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Inside the horizon, these black holes resemble the interior of a holographic superconductor. There are analogs of the Josephson oscillations of the scalar field, and the final Kasner singularity depends very sensitively on the black hole parameters near the onset of the instability. In an Appendix, we give a general argument that Cauchy horizons cannot exist in a large class of stationary black holes with scalar hair.
We study the geodesics of a five dimensional non-asymptotically flat dilatonic 2-brane. Although the metric's warp function diverges logarithmically in the far field region of the transverse space, the curvature does not. The brane has two naked singularities, the usual central singularity and a circular singularity at the radius where the warp function vanishes. This creates two causally disconnected regions of the transverse space. Using the methods of energy conservation and effective potentials we study the null and timelike orbital and radial geodesics in both regions and show that they e…
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…
In the framework of string-inspired dilatonic gravity theories (from 4 to $D$ space-time dimensions), we construct new non-asymptotically flat black hole or black brane solutions. For particular values of the dilatonic coupling constant, we generalize static solutions to rotating ones, using the target space isometry group. We compute their masses and their angular momentum using the modern approach to the computation of energy in General Relativity, the quasilocal formalism, and we check the agreement of these solutions with the first law of black hole thermodynamics. Finally, we study a new …
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.
A novel criterion to determine the presence of gravitational radiation arriving to, or departing from, null infinity of any weakly asymptotically-simple space-time with vanishing cosmological constant is given. The quantities involved are geometric, of tidal nature, with good gauge behaviour and univocally defined at null infinity. The relationship with the classical characterisation using the News tensor is analysed in detail. A new balance law at infinity is presented, which may be useful to define `radiation states'.
The situation with asymptotically flat gravitating spinor field solutions is considered. It is supposed that the problem of constructing these solutions is connected with confinement problem in quantum chromodynamics. It is argued that in both cases we must use a nonperturbative quantum technique.
In a recent paper, Hod started a study on no scalar hair theorem for asymptotically flat spherically symmetric neutral horizonless reflecting compact stars. In fact, Hod's approach only rules out massive scalar fields. In the present paper, for massless scalar fields outside neutral horizonless reflecting compact stars, we provide a rigorous mathematical proof on no hair theorem. We show that asymptotically flat spherically symmetric neutral horizonless reflecting compact stars cannot support exterior massless scalar field hairs.
We propose a quasi-local stress tensor for the four-dimensional asymptotically flat Robinson-Trautman geometries by taking the flat-space limit from the corresponding asymptotically AdS solutions. This stress tensor results in the correct charges of the generators of BMS symmetry if we define conformal infinity by an anisotropic scaling of the metric components. Using flat-space holography this stress tensor is related to expectation values of the stress tensor in a dual field theory called BMS-invariant field theory (BMSFT). We also calculate the two and three point functions of the proposed …
We consider asymtotically anti-de Sitter spacetimes in general dimensions. We review the origin of infrared divergences in the on-shell gravitational action, and the construction of the renormalized on-shell action by the addition of boundary counterterms. In odd dimensions, the renormalized on-shell action is not invariant under bulk diffeomorphisms that yield conformal transformations in the boundary (holographic Weyl anomaly). We obtain formulae for the gravitational stress energy tensor, defined as the metric variation of the renormalized on-shell action, in terms of coefficients in the as…
Certain non-asymptotically flat but supersymmetric classical solution of the type IIA supergravity can be interpreted as the infinitely-boosted version of the D-particle solution along the M-theory circle. By a chain of T-dual transformations, this analysis also applies to yield non-asymptotically flat solutions from the asymptotically flat and (non)-extremal solutions with intersecting D-strings and D five-branes of the type IIB supergravity compactified on a five-torus. Under S-duality, the non-asymptotically flat solutions in this context can in particular be used to describe the (1+1)-dime…
The recently proposed theory of "Asymptotically Free Mimetic Gravity" is extended to the general non-homogeneous, spatially non-flat case. We present a modified theory of gravity which is free of higher derivatives of the metric. In this theory asymptotic freedom of gravity implies the existence of a minimal black hole with vanishing Hawking temperature. Introducing a spatial curvature dependent potential, we moreover obtain non-singular, bouncing modifications of spatially non-flat Friedmann and Bianchi universes.
We study static brane configurations in the bulk background of the topological black holes in asymptotically flat spacetime. We find that such configurations are possible even for flat black hole horizon, unlike the AdS black hole case. We construct the brane world model with an orbifold structure S^1/Z_2 in such bulk background. We also study massless bulk scalar field.
We present results from the evolution of spacetimes that describe the merger of asymptotically global AdS black holes in 5D with an SO(3) symmetry. Prompt scalar field collapse provides us with a mechanism for producing distinct trapped regions on the initial slice, associated with black holes initially at rest. We evolve these black holes towards a merger, and follow the subsequent ring-down. The boundary stress tensor of the dual CFT is conformally related to a stress tensor in Minkowski space which inherits an axial symmetry from the bulk SO(3). We compare this boundary stress tensor to its…
We derive new rotating, non-asymptotically flat black ring solutions in five-dimensional Einstein-Maxwell-dilaton gravity with dilaton coupling constant $α=\sqrt{8/3}$ which arises from a six-dimensional Kaluza-Klein theory. As a limiting case we also find new rotating, non-asymptotically flat five-dimensional black holes. The solutions are analyzed and the mass, angular momentum and charge are computed. A Smarr-like relation is found. It is shown that the first law of black hole thermodynamics is satisfied.
In this work we present a "modest" holographic reconstruction of the bulk geometry in asymptotically flat spacetime using the two-point correlators of boundary quantum field theory (QFT) in asymptotically flat spacetime. The boundary QFT lives on the null boundary of the spacetime, namely null infinity and/or the Killing horizons. The bulk reconstruction relies on two unrelated results: (i) there is a bulk-to-boundary type correspondence between free quantum fields living in the bulk manifold and free quantum fields living on its null boundary, and (ii) one can construct the metric by making u…
Making use of the conformal positive energy theorem we prove the uniqueness of four-dimensional static electrically charged black holes being the solution of Chern-Simons dynamical gravity equations of motion. We assume that black hole spacetime contains an asymptotically flat spacelike hypersurface with compact interior and non-degenerate components of the event horizon.
We discuss some recent results in the quest to implement the holographic principle in asymptotically flat spacetimes. In particular we introduce the key ingredients of the candidate dual theory which lives at null infinity and it is invariant under the asymptotic symmetry group of this class of spacetimes.
Recently, Klemm and others [hep-th/0104141] have successfully generalized the Cardy-Verlinde formula for an asymptotically flat spacetime of arbitrary dimensionality. And yet, from a holographic perspective, the interpretation of this formula remains somewhat unclear. Nevertheless, in this paper, we incorporate the implied flat space/CFT duality into a study on boundary descriptions of a $d$-dimensional Schwarzschild-black hole spacetime. In particular, we demonstrate that the (presumably) dual CFT adopts a string-like description and, moreover, is thermodynamically equivalent to a string that…
We propose a stress tensor for the Kerr black hole written in the Boyer-Lindquist coordinate. To achieve this, we use the dictionary of the Flat/CCFT correspondence and take the flat-space limit from the quasi-local stress tensor of the four-dimensional Kerr-AdS black hole. The proposed stress tensor yields the correct values for the mass and angular momentum of the Kerr black hole at spatial infinity. We also calculate some components of the energy momentum tensor of the three dimensional CCFT and show that they are consistent with the holographic calculation of the Kerr black hole. The calcu…
We study the thermodynamics of the asymptotically flat static black hole in Lovelock back ground where the coupling constants of the Lovelock theory effects are taken into account. We consider the effects of the second order of the coupling constant, and third order of the Lovelock constant coefficient on the thermodynamics of asymptotically flat static black holes. In this case the effect of the coupling constants on the thermodynamics of the black hole are discussed for 5, 6, and 7 dimensional spacetime.
We propose a holographic duality for a four dimensional WZW model with target manifold $\mathrm{SO}(8)$, coupled to scalar-flat Kähler gravity on an asymptotically flat, four dimensional background known as the Burns metric. The holographic dual is a two dimensional chiral algebra built out of gauged beta-gamma systems with $\mathrm{SO}(8)$ flavor. We test the duality by matching two-point correlators of soft gluon currents with two-point gluon amplitudes, and their leading OPE coefficients with collinear limits of three-point gluon amplitudes.
We study Ricci flows on $R^n$, $n\ge 3$, that evolve from asymptotically flat initial data. Under mild conditions on the initial data, we show that the flow exists and remains asymptotically flat for an interval of time. The mass is constant in time along the flow. We then specialize to the case of rotationally symmetric, asymptotically flat initial data containing no embedded minimal hyperspheres. We show that in this case the flow is immortal, remains asymptotically flat, never develops a minimal hypersphere, and converges to flat Euclidean space as the time diverges to infinity. We discuss …
We compute the boundary stress tensor associated with Mann-Marolf counterterm in asymptotic flat and static spacetime for cylindrical boundary surface as $r \rightarrow \infty$, and find that the form of the boundary stress tensor is the same as the hyperbolic boundary case in 4 dimensions, but has additional terms in higher than 4 dimensions. We find that these additional terms are impotent and do not contribute to conserved charges. We also check the conservation of the boundary stress tensor in a sense that $\mathcal{D}^a T_{ab} = 0$, and apply our result to the ($n+3$)-dimensional static b…
