Solutions Of New Massive Gravity Research Articles

Thin-shells and thin-shell wormholes in new massive gravity

Within 2 + 1-dimensional cosmological new massive gravity, we consider thin-shell and thin-shell wormhole construction. For this, we introduce first, the junction conditions apt for the fourth order terms in the action of the theory. Then, by employing some specific static solutions in new massive gravity, we study the characteristics of associated thin-shells and thin-shell wormholes. Our finding suggests that, firstly, there cannot exist any thin-shells regarding our chosen solutions of cosmological new massive gravity, and secondly, the constructed thin-shell wormhole does not need to be symmetric. More importantly, the thin-shell wormhole, if ever forms, possesses null energy density and null angular pressure on its throat which are preferable to their negative-valued counterparts.

Anisotropic scale invariant spacetimes and black holes in Zwei-Dreibein Gravity

We show that Zwei-Dreibein Gravity (ZDG), a bigravity theory recently proposed by Bergshoeff, de Haan, Hohm, Merbis, and Townsend in Phys.Rev.Lett. 111 (2013) 111102, admits exact solutions with anisotropic scale invariance. These type of geometries are the three-dimensional analogues of the spacetimes which were proposed as gravity duals for condensed matter systems. In particular, we find Schr\"odinger invariant spaces as well as Lifshitz spaces with arbitrary dynamical exponent $z$. We also find black holes that are asymptotically Lifshitz with $z=3$, showing that these (non-constant curvature) solutions of New Massive Gravity (NMG) are persistent after the introduction of the infinite tower of higher-curvature terms of ZDG, provided a renormalization of the parameters. Black holes in asymptotically warped Anti-de Sitter spaces are also found. Interestingly, in almost all the geometries studied in this work, the metric associated with the second dreibein turns out to be equivalent, up to a constant global factor, to the first one. This phenomenon has been previously observed in other bigravity theories in asymptotically flat and asymptotically Anti-de Sitter backgrounds. However, for the particular case of the $z=3$ Lifshitz black hole, here we found that the second metric corresponds to a different black hole that coincides with the former only in the asymptotic region. In fact, we find a new family of $z=3$ black holes that corresponds to a one-parameter deformation of the NMG solution.

Towards the uniqueness of Lifshitz black holes and solitons in new massive gravity

We prove that the z=1 and z=3 Lifshitz black hole solutions of New Massive Gravity in three dimensions are the only static axisymmetric solutions that can be cast in a Kerr-Schild form with a seed metric given by the Lifshitz spacetime. Correspondingly, we study the issue of uniqueness of Lifshitz solitons when considering an ansatz involving a single metric function. We show this problem can be mapped to the previous one and that the z=1 and z=1/3 Lifshitz soliton solutions are the only ones within this class. Finally, our approach suggests for the first time an explanation as to what is special about those particular values of the dynamical critical exponent z at finite temperature.

Non-perturbative Massive Solutions in Gravitational Higgs Mechanism

We construct exact non-perturbative massive solutions in the gravitational Higgs mechanism. They confirm the conclusions of arXiv:1102.4991, which are based on non-perturbative Hamiltonian analysis for the rel- evant metric degrees of freedom, that while perturbatively unitarity may not be evident, no negative norm state is present in the full nonlinear theory. The non-perturbative massive solutions do not appear to exhibit instabil- ities and describe vacuum configurations which are periodic in time, including purely longitudinal solutions with isotropic periodically expanding and contracting spatial dimensions, cosmological strings with only one peri- odically expanding and contracting spatial dimension, and also purely non-longitudinal (traceless) periodically expanding and contracting solutions with constant spatial volume. As an aside we also discuss massive solutions in New Massive Gravity. While such solutions are present in the linearized theory, we argue that already at the next-to-linear (quadratic) order in the equations of motion (and, more generally, for weak-field configurations) there are no massive solutions.

Extremal black holes and holographic c-theorem

We found Bogomolʼnyi type of the first order differential equations in three-dimensional Einstein gravity and the effective second order ones in new massive gravity when an interacting scalar field is minimally coupled. Using these equations in Einstein gravity, we obtain analytic solutions corresponding to extremally rotating hairy black holes. We also obtain perturbatively extremal black hole solutions in new massive gravity using these lower order differential equations. All these solutions have the anti-de Sitter spaces as their asymptotic geometries and as the near horizon ones. This feature of solutions interpolating two anti-de Sitter spaces leads to the construction of holographic c-theorem in these cases. Since our lower order equations reduce naturally to the well-known equations for domain walls, our results can be regarded as the natural extension of domain walls to more generic cases.

Covariant symplectic structure and conserved charges of new massive gravity

We show that the symplectic current obtained from the boundary term, which arises in the first variation of a local diffeomorphism invariant action, is covariantly conserved for any gravity theory described by that action. Therefore, a Poincare invariant 2-form can be constructed on the phase space, which is shown to be closed without reference to a specific theory. Finally, we show that one can obtain a charge expression for gravity theories in various dimensions, which plays the role of the Abbott-Deser-Tekin (ADT) charge for spacetimes with non-constant curvature backgrounds, by using the diffeomorphism invariance of the symplectic 2-form. As an example, we calculate the conserved charges of some solutions of New Massive Gravity (NMG) and compare the results with the previous works.

TypeDsolutions of 3D new massive gravity

In a recent reformulation of three-dimensional new massive gravity (NMG), the field equations of the theory consist of a massive (tensorial) Klein-Gordon type equation with a curvature-squared source term and a constraint equation. Using this framework, we present all algebraic type D solutions of NMG with constant and nonconstant scalar curvatures. For constant scalar curvature, they include homogeneous anisotropic solutions which encompass both solutions originating from topologically massive gravity (TMG), Bianchi types II, VIII, IX, and those of non-TMG origin, Bianchi types VI_{0} and VII_{0} . For a special relation between the cosmological and mass parameters, \lambda=m^2, they also include conformally flat solutions, and in particular those being locally isometric to the previously-known Kaluza-Klein type AdS_2xS^1 or dS_2x S^1 solutions. For nonconstant scalar curvature, all the solutions are conformally flat and exist only for \lambda=m^2 . We find two general metrics which possess at least one Killing vector and comprise all such solutions. We also discuss some properties of these solutions, delineating among them black hole type solutions.

The general type N solution of new massive gravity

We find the most general algebraic type N solution with non-vanishing scalar curvature, which comprises all type N solutions of new massive gravity in three dimensions. We also give the special forms of this solution, which correspond to certain critical values of the topological mass. Finally, we show that at the special limit, the null Killing isometry of the spacetime is restored and the solution describes AdS pp-waves.

Boundary stress tensor and counterterms for weakened AdS3 asymptotic in New Massive Gravity

Resorting to the notion of a stress-tensor induced on the boundary of a space-time, we compute the conserved charges associated to exact solutions of New Massive Gravity that obey weakened versions of AdS3 asymptotic boundary conditions. The computation requires the introduction of additional counterterms, which play the rôle of regularizing the semiclassical stress-tensor in the boundary theory. We show that, if treated appropriately, different ways of prescribing asymptotically AdS3 boundary conditions yield finite conserved charges for the solutions. The consistency of the construction manifests itself in that the charges of hairy asymptotically AdS3 black holes computed by this holography-inspired method exactly match the values required for the Cardy formula to reproduce the black hole entropy. We also consider new solutions to the equations of motion of New Massive Gravity, which happen to fulfill Brown-Henneaux boundary conditions despite not being Einstein manifolds. These solutions are shown to yield vanishing boundary stress-tensor. The results obtained in this paper can be regarded as consistency checks for the prescription proposed in [1].

Black holes with a null Killing vector in three-dimensional massive gravity

We investigate solutions of new massive gravity with two commuting Killing vectors, one of which is null, with a special emphasis on black hole solutions. Besides extreme BTZ black holes and, for a special value of the coupling constant, massless null warped black holes, we also obtain for a critical coupling a family of massive ‘log’ black holes. These are asymptotic to the extreme BTZ black holes in the sense of log gravity.