Bachian gravity in three dimensions

In a recent paper [1], we explored the space of solutions of the exotic massive 3D gravity theory proposed in [2]. We showed that the theory admits a rich space of vacua, including asymptotically Anti de-Sitter (AdS) geometries obeying different types of boundary conditions. The examples include black holes dressed with low decaying gravitons. Based on what happens in other theories of massive gravity, we conjectured that such geometries appear on a curve of the parameter space (chiral curve) where the exotic massive gravity on AdS with sufficiently strong boundary conditions results dual to a 2D chiral conformal field theory. Here, we show that this expectation is consistent with the conserved charges and thermodynamical properties of the black holes of the theory, which have recently been computed [3]. When the boundary conditions are relaxed relative to the standard Brown-Henneaux boundary conditions, the theory exhibits solutions consistent with the definition of the so-called Log-gravity. The asymptotic behavior of these solutions presents a logarithmic term in the Fefferman-Graham expansion that, nonetheless, is compatible with the AdS asymptotic symmetries. This long range interaction is due to a mode of the massive gravity that becomes massless precisely on the chiral curve.We construct exact solutions exhibiting this behavior, which admit to be interpreted as fully backreacting gravitational waves propagating on an extremal black hole, and carrying nonvanishing gravitational energy. We also discuss other vacua of the theory, such as Warped-AdS 3 black holes, gravitational waves on such backgrounds, AdS 2 × S 1 spaces, and black holes in dS 3 space.

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“…The conserved charges of the BTZ solution in EMG were recently computed in [3] (see also [11]), being the energy…”

Section: Introductionmentioning

confidence: 99%

More on vacua of exotic massive 3D gravity

Giribet

Oliva

2019

Phys. Rev. D

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“…Finally, there is a class of 3D gravity models that do not have a corresponding metric formulation with a single metric. These models are referred to as the third-way consistent models and they play an essential role in the resolution of the 'bulk vs boundary clash in three dimensions [38][39][40][41][42]. Our procedure does not include these models and it would be very interesting to see if there is an algebra that underlies the third way to gravity models.…”

Section: Jhep01(2022)010mentioning

confidence: 99%

The holographic c-theorem and infinite-dimensional Lie algebras

Bergshoeff

Ozkan

Zog

2022

J. High Energ. Phys.

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We discuss a non-dynamical theory of gravity in three dimensions which is based on an infinite-dimensional Lie algebra that is closely related to an infinite-dimensional extended AdS algebra. We find an intriguing connection between on the one hand higher-derivative gravity theories that are consistent with the holographic c-theorem and on the other hand truncations of this infinite-dimensional Lie algebra that violate the Lie algebra structure. We show that in three dimensions different truncations reproduce, up to terms that do not contribute to the c-theorem, Chern-Simons-like gravity models describing extended 3D massive gravity theories. Performing the same procedure with similar truncations in dimensions larger than or equal to four reproduces higher derivative gravity models that are known in the literature to be consistent with the c-theorem but do not have an obvious connection to massive gravity like in three dimensions.

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“…(105) with (η ν ρ − 1 μ ρ αν ∂ α ) we obtain − μ 2 h μν = 0. (106) Equation ( 96) describes the propagation of one degree of freedom, a massive spin-2 graviton with mass m = μ 2 [25], now the solutions are even more general than Einstein's metrics [26]. In this respect, the TMG theory is attractive because it is close to real gravity.…”

Section: Appendix Bmentioning

confidence: 99%

New canonical analysis for higher order topologically massive gravity

Escalante

Aguilar

2021

Eur. Phys. J. C

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A detailed Gitman–Lyakhovich–Tyutin analysis for higher-order topologically massive gravity is performed. The full structure of the constraints, the counting of physical degrees of freedom, and the Dirac algebra among the constraints are reported. Moreover, our analysis presents a new structure into the constraints and we compare our results with those reported in the literature where a standard Ostrogradski framework was developed.

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Bachian gravity in three dimensions

Cited by 20 publications

References 37 publications

More on vacua of exotic massive 3D gravity

More on vacua of exotic massive 3D gravity

The holographic c-theorem and infinite-dimensional Lie algebras

New canonical analysis for higher order topologically massive gravity

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