Anisotropic Scale Invariant Spacetimes and Black Holes in Zwei-Dreibein Gravity

Abstract

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 Schrödinger 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.

arXiv comment1+15 pages. v2 minor corrections, version published in JHEP

References in corpus (31)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• The World as a Hologram
• The Black Hole in Three Dimensional Space Time
• Building an AdS/CFT superconductor
• Lectures on holographic methods for condensed matter physics
• Gravity Duals of Lifshitz-like Fixed Points
• Massive Gravity in Three Dimensions
• Bimetric Gravity from Ghost-free Massive Gravity
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Logarithmic Operators in Conformal Field Theory
• More on Massive 3D Gravity
• Warped Conformal Field Theory
• Lifshitz Black Hole in Three Dimensions
• Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity
• Warped AdS_3 black holes in new massive gravity
• Bending AdS Waves with New Massive Gravity
• A boundary stress tensor for higher-derivative gravity in AdS and Lifshitz backgrounds
• Covariant constraints in ghost free massive gravity
• Higher Derivative Gravity and Conformal Gravity From Bimetric and Partially Massless Bimetric Theory
• Zwei-Dreibein Gravity
• Boundary stress tensor and counterterms for weakened AdS_3 asymptotic in New Massive Gravity
• The Boulware-Deser mode in Zwei-Dreibein gravity
• Warped black holes in 3D general massive gravity
• Hairy black holes in theories with massive gravitons
• Three-dimensional massive gravity and the bigravity black hole
• Towards the uniqueness of Lifshitz black holes and solitons in New Massive Gravity
• Logarithmic AdS Waves and Zwei-Dreibein Gravity
• The Brown-York mass of black holes in Warped Anti-de Sitter space
• Boundary stress tensor and asymptotically AdS3 non-Einstein spaces at the chiral point

Cited by in corpus (7)

• Interacting spin-2 fields in three dimensions
• Warped-AdS3 black holes with scalar halo
• Conserved charges in timelike Warped-AdS${}_3$ spaces
• Constructing entanglement wedges for Lifshitz spacetimes with Lifshitz gravity
• Energy-entropy relation for asymptotically Lifshitz spacetimes with universal horizons
• Critical points of WAdS/CFT and higher-curvature gravity
• The mass of a Lifshitz black hole