New Massive Gravity Research Articles

Solutions with pure radiation and gyratons in 3D massive gravity theories

We find exact solutions of topologically massive gravity (TMG) and new massive gravity (NMG) in 2 + 1 dimensions (3D) with an arbitrary cosmological constant, pure radiation, and gyratons, i.e. with possibly non-zero T uu and T ux in canonical coordinates. Since any ‘reasonable’ geometry in 3D (i.e. admitting a null geodesic congruence) is either expanding Robinson–Trautman ( Θ≠0 ) or Kundt ( Θ=0 ), we focus on these two classes. Assuming expansions Θ=1/r (‘GR-like’ Robinson–Trautman) or Θ=0 (general Kundt), we systematically integrate the field equations of TMG and NMG and identify new classes of exact solutions. The case of NMG contains an additional assumption of g ux being quadratic in r, which is automatically enforced in TMG as well as in 3D GR. In each case, we reduce the field equations as much as possible and identify new classes of solutions. We also discuss various special subclasses and study some explicit solutions.

Causality of 3D extended gravity theories

Causality is one of the most important properties to understand gravity theories. It gives us not only a method to confirm that the gravity theories are really consistent, but also gives implications about the properties which unknown fundamental physics should obey. We investigate the causality of three-dimensional (3D) gravity theories, which are considered to be important, by using the Shapiro time delay effect in the Shock wave geometry. One of such gravity theories is the Zwei-Dreibein Gravity (ZDG) theory, which is a consistent 3D gravity theory. In ZDG theory, the serious problems can be removed that have appeared in another important gravity theory called New Massive Gravity (NMG). We study whether the ZDG theory could preserve the causality without losing the above good properties and how the causality structure is related to the structure of the NMG theory.

Complexity growth in massive gravity theories, the effects of chirality, and more

To study the effect of parity violation on the rate of complexity growth, by using ``$\text{complexity}=\text{action}$'' conjecture, we find the complexity growth rates in different solutions of the chiral theory of topologically massive gravity (TMG) and parity-preserving theory of new massive gravity (NMG). Using the results, one can see that decreasing the parameter $\ensuremath{\mu}$, which increases the effect of the Chern-Simons term and increases chirality, would increase the rate of growth of complexity. Also one can observe a stronger correlation between complexity growth and temperature rather than complexity growth and entropy. At the end we comment on the possible meaning of the deforming term of chiral Liouville action for the rate of complexity growth of warped conformal field theories in the tensor network renormalization picture.

Weyl and transverse diffeomorphism invariant spin-2 models in D=2+1

There are two covariant descriptions of massless spin-2 particles in D=3+1 via a symmetric rank-2 tensor: the linearized Einstein–Hilbert (LEH) theory and the Weyl plus transverse diffeomorphism (WTDIFF) invariant model. From the LEH theory one can obtain the linearized new massive gravity (NMG) in D=2+1 via Kaluza–Klein dimensional reduction followed by a dual master action. Here we show that a similar route takes us from the WTDIFF model to a linearized scalar–tensor NMG which belongs to a larger class of consistent spin-0 modifications of NMG. We also show that a traceless master action applied to a parity singlet furnishes two new spin-2 self-dual models. Moreover, we examine the singular replacement h_{mu nu } rightarrow h_{mu nu } - eta _{mu nu }h/D and prove that it leads to consistent massive spin-2 models in D=2+1. They include linearized versions of unimodular topologically massive gravity (TMG) and unimodular NMG. Although the free part of those unimodular theories are Weyl invariant, we do not expect any improvement in the renormalizability. Both the linearized K-term (in NMG) and the linearized gravitational Chern–Simons term (in TMG) are invariant under longitudinal reparametrizations delta h_{mu nu } = partial _{mu }partial _{nu }zeta , which is not a symmetry of the WTDIFF Einstein–Hilbert term. Therefore, we still have one degree of freedom whose propagator behaves like 1/p^2 for large momentum.

Relating renormalizability of D-dimensional higher-order electromagnetic and gravitational models to the classical potential at the origin

Simple prescriptions for computing the D-dimensional classical potential related to electromagnetic and gravitational models, based on the functional generator, are built out. These recipes are employed afterward as a support for probing the premise that renormalizable higher-order systems have a finite classical potential at the origin. It is also shown that the opposite of the conjecture above is not true. In other words, if a higher-order model is renormalizable, it is necessarily endowed with a finite classical potential at the origin, but the reverse of this statement is untrue. The systems used to check the conjecture were D-dimensional fourth-order Lee–Wick electrodynamics, and the D-dimensional fourth- and sixth-order gravity models. A special attention is devoted to New Massive Gravity (NMG) since it was the analysis of this model that inspired our surmise. In particular, we made use of our premise to resolve trivially the issue of the renormalizability of NMG, which was initially considered to be renormalizable, but it was shown some years later to be non-renormalizable. We remark that our analysis is restricted to local models in which the propagator has simple and real poles.

New Bi-Gravity from New Massive Gravity

Using the action of three dimensional New Massive Gravity (NMG) we construct a new bi-gravity in three dimensions. This can be done by promoting the rank two auxiliary field appearing in the expression of NMG's action into a dynamical field. We show that small fluctuations around the AdS vacuum of the model are non-tachyonic and ghost free within certain range of the parameters of the model. We study central charges of the dual field theory and observe that in this range they are positive too. This suggests that the proposed model might be a consistent three dimensional bi-gravity.

Bulk and boundary unitary gravity in 3D:MMG2

We construct a massive spin-2 theory in 2+1 dimensions that is immune to the bulk-boundary unitarity conflict in anti-de Sitter space and hence amenable to holography. The theory is an extension of Topologically Massive Gravity, just like the recently found Minimal Massive Gravity (MMG), but it has two massive helicity modes instead of a single one. The theory admits all the solutions of TMG with a redefined topological parameter. We calculate the Shapiro time-delay and show that flat-space (local) causality is not violated. We show that there is an interesting relation between the theory we present here (which we call MMG$_2$), MMG and the earlier New Massive Gravity (NMG): Namely, field equations of these theories are non-trivially related. We study the bulk excitations and boundary charges of the conformal field theory that could be dual to gravity. We also find the chiral gravity limit for which one of the massive modes becomes massless. The virtue of the model is that one does not have to go to the chiral limit to achieve unitarity in the bulk and on the boundary and the log-terms that appear in the chiral limit and cause instability do not exist in the generic theory.

Conserved charges in timelike warpedAdS3spaces

We consider the timelike version of warped anti--de Sitter space (WAdS), which corresponds to the three-dimensional section of the G\"odel solution of four-dimensional cosmological Einstein equations. This geometry presents closed timelike curves (CTCs), which are inherited from its four-dimensional embedding. In three dimensions, this type of solution can be supported without matter provided the graviton acquires mass. Here, among the different ways to consistently give mass to the graviton in three dimensions, we consider the parity-even model known as new massive gravity (NMG). In the bulk of timelike ${\mathrm{WAdS}}_{3}$ space, we introduce defects that, from the three-dimensional point of view, represent spinning massive particlelike objects. For this type of source, we investigate the definition of quasilocal gravitational energy as seen from infinity, far beyond the region where the CTCs appear. We also consider the covariant formalism applied to NMG to compute the mass and the angular momentum of spinning particlelike defects and compare the result with the one obtained by means of the quasilocal stress tensor. We apply these methods to special limits in which the ${\mathrm{WAdS}}_{3}$ solutions coincide with locally ${\mathrm{AdS}}_{3}$ and locally ${\mathrm{AdS}}_{2}\ifmmode\times\else\texttimes\fi{}\mathbb{R}$ spaces. Finally, we make some comments about the asymptotic symmetry algebra of asymptotically ${\mathrm{WAdS}}_{3}$ spaces in NMG.

Holographic entropy of Warped-AdS3 black holes

We study the asymptotic symmetries of three-dimensional Warped Anti-de Sitter (WAdS) spaces in three-dimensional New Massive Gravity (NMG). For a specific choice of asymptotic boundary conditions, we find that the algebra of charges is infinite dimensional and coincides with the semidirect sum of Virasoro algebra with non-vanishing central charge and an affine û(1) k Kač-Moody algebra. We show that the WAdS black hole configurations organize in terms of two commuting Virasoro algebras. We identify the Virasoro generators that expand the associated representations in the dual Warped Conformal Field Theory (WCFT) and, by applying the Warped version of the Cardy formula, we prove that the microscopic WCFT computation exactly reproduces the entropy of black holes in WAdS space.

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.

Aspects of warped AdS3/CFT2 correspondence

In this paper we apply the thermodynamics method to investigate the holographic pictures for the BTZ black hole, the spacelike and the null warped black holes in three-dimensional topologically massive gravity (TMG) and new massive gravity (NMG). Even though there are higher derivative terms in these theories, the thermodynamics method is still effective. It gives consistent results with the ones obtained by using asymptotical symmetry group (ASG) analysis. In doing the ASG analysis we develop a brute-force realization of the Barnich-Brandt-Compere formalism with Mathematica code, which also allows us to calculate the masses and the angular momenta of the black holes. In particular, we propose the warped AdS$_3$/CFT$_2$ correspondence in the new massive gravity, which states that quantum gravity in the warped spacetime could holographically dual to a two-dimensional CFT with $c_R=c_L=\f{24}{Gm\b^2\sr{2(21-4\b^2)}}$.

Non-Fefferman-Graham asymptotics and holographic renormalization in new massive gravity

The asymptotic behavior of new massive gravity (NMG) is analyzed for all values of the mass parameter satisfying the Breitenlohner-Freedman bound. The traditional Fefferman-Graham expansion fails to capture the dynamics of NMG, and new terms in the asymptotic expansion are needed to include the massive graviton modes. New boundary conditions are discovered for a range of values $-1<2m^2l^2<1$ at which non-Einstein modes decay more slowly than the Brown-Henneaux boundary conditions. The holographically renormalized stress tensor is computed for these modes, and the relevant counterterms are identified up to unphysical ambiguities.

Fermions Tunneling Mechanism for a New Class of Black Holes in EGB Gravity and Three-Dimensional Lifshitz Black Hole

The objective of this paper is to investigate the Fermions tunneling radiation of a new class of black holes in Einstein-Gauss-Bonnet (EGB) gravity and three-dimensional Lifshitz black hole in New Massive Gravity (NMG). As a result, the tunneling probability and Hawking temperature of the black holes are well recovered, which confirms that the Hawking temperature of emitted Dirac particles of the black holes are the same as in the case of scalar particles. The quantization of entropy from the black hole have also been discussed.

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.

Type N spacetimes as solutions of extended new massive gravity

We study algebraic type N spacetimes in the extended new massive gravity (NMG), considering both the Born-Infeld model (BI-NMG) and the model of NMG with any finite order curvature corrections. We show that for these spacetimes, the field equations of BI-NMG take the form of the massive (tensorial) Klein–Gordon type equation, just as it happens for ordinary NMG. This fact enables us to obtain the type N solution to BI-NMG, utilizing the general type N solution of NMG, earlier found in our work. We also obtain type N solutions to NMG with all finite order curvature corrections and show that, in contrast to BI-NMG, this model admits the critical point solutions, which are counterparts of “logarithmic” AdS pp-waves solutions of NMG.

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.

All bulk and boundary unitary cubic curvature theories in three dimensions

We construct all the bulk and boundary unitary cubic curvature parity invariant gravity theories in three dimensions in (anti)-de Sitter spaces. For bulk unitarity, our construction is based on the principle that the free theory of the cubic curvature theory reduces to one of the three known unitary theories which are the cosmological Einstein-Hilbert theory, the quadratic theory of the scalar curvature or the new massive gravity (NMG). Bulk and boundary unitarity in NMG is in conflict; therefore, cubic theories that are unitary both in the bulk and on the boundary have free theories that reduce to the other two alternatives. We also study the unitarity of the Born-Infeld extensions of NMG to all orders in curvature.

Exact Solutions in 3D New Massive Gravity

We show that the field equations of new massive gravity (NMG) consist of a massive (tensorial) Klein-Gordon-type equation with a curvature-squared source term and a constraint equation. We also show that, for algebraic type D and N spacetimes, the field equations of topologically massive gravity (TMG) can be thought of as the "square root" of the massive Klein-Gordon-type equation. Using this fact, we establish a simple framework for mapping all types D and N solutions of TMG into NMG. Finally, we present new examples of types D and N solutions to NMG.

Holographic renormalization of new massive gravity

We study holographic renormalization for three dimensional new massive gravity (NMG). By studying the general fall off conditions for the metric allowed by the model at infinity, we show that at the critical point where the central charges of the dual CFT are zero it contains a leading logarithmic behavior. In the context of AdS/CFT correspondence it can be identified as a source for an irrelevant operator in the dual CFT. The presence of the logarithmic fall off may be interpreted as the fact that the dual CFT would be a LCFT.

Charged black holes in new massive gravity

We construct charged black hole solutions to three-dimensional new massive gravity (NMG), by adding electromagnetic Maxwell and Chern–Simons actions. We find charged black holes in the form of warped AdS3 and “log” solutions in specific critical point. The entropy, mass and angular momentum of these black holes are computed.