Lower-dimensional Horava-Lifshitz gravity
arXiv:1103.3013 · doi:10.1103/PhysRevD.83.124021
Abstract
We consider Horava-Lifshitz gravity in both 1+1 and 2+1 dimensions. These lower-dimensional versions of Horava-Lifshitz gravity are simple enough to be explicitly tractable, but still complex enough to be interesting. We write the most general (non-projectable) action for each case and discuss the resulting dynamics. In the 1+1 case we utilize the equivalence with 2-dimensional Einstein-aether theory to argue that, even though non-trivial, the theory does not have any local degrees of freedom. In the 2+1 case we show that the only dynamical degree of freedom is a scalar, which qualitatively has the same dynamical behaviour as the scalar mode in (non-projectable) Horava-Lifshitz gravity in 3+1 dimensions. We discuss the suitability of these lower-dimensional theories as simpler playgrounds that could help us gain insight into the 3+1 theory. As special cases we also discuss the projectable limit of these theories. Finally, we present an algorithm that extends the equivalence with (higher order) Einstein-aether theory to full Horava-Lifshitz gravity (instead of just the low energy limit), and we use this extension to comment on the apparent naturalness of the covariant formulation of the latter.
v2: 9 pages, discussion about projectable version as a limiting case added; v3: minor changes to match published version
References in corpus (29)
- Quantum Gravity at a Lifshitz Point
- Gravity with a dynamical preferred frame
- Membranes at Quantum Criticality
- A healthy extension of Horava gravity
- Models of non-relativistic quantum gravity: the good, the bad and the healthy
- Strong coupling in Horava gravity
- Horava-Lifshitz Cosmology: A Review
- Quantum gravity without Lorentz invariance
- On the Extra Mode and Inconsistency of Horava Gravity
- Phenomenologically viable Lorentz-violating quantum gravity
- Lorentz symmetry breaking as a quantum field theory regulator
- General Covariance in Quantum Gravity at a Lifshitz Point
- Horava-Lifshitz gravity: a status report
- Extended Horava gravity and Einstein-aether theory
- Comment on `Strong coupling in extended Horava-Lifshitz gravity'
- Cosmological perturbations in Horava-Lifshitz theory without detailed balance
- A Trouble with Hořava-Lifshitz Gravity
- A dynamical inconsistency of Horava gravity
- Strong coupling in extended Horava-Lifshitz gravity
- Cuscuton and low energy limit of Horava-Lifshitz gravity
- Relativistic Quantum Gravity at a Lifshitz Point
- Pathological behaviour of the scalar graviton in Hořava-Lifshitz gravity
- General Covariance in Gravity at a Lifshitz Point
- Lessons from the decoupling limit of Horava gravity
- On the infrared limit of Horava's gravity with the global Hamiltonian constraint
- Projectable Horava-Lifshitz gravity in a nutshell
- Stability of spin-0 graviton and strong coupling in Horava-Lifshitz theory of gravity
- Is nonrelativistic gravity possible?
- Two-dimensional gravity with a dynamical aether
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- Scale hierarchy in Horava-Lifshitz gravity: a strong constraint from synchrotron radiation in the Crab nebula
- Rotating black holes in three-dimensional Hořava gravity
- Status of Horava gravity: A personal perspective
- One-loop renormalization in a toy model of Horava-Lifshitz gravity
- Revisiting the cuscuton as a Lorentz-violating gravity theory
- Spacetime condensation in (2+1)-dimensional CDT from a Horava-Lifshitz minisuperspace model
- Evolution and spherical collapse in Einstein-aether theory and Horava gravity
- Superradiance in dispersive black hole analogues
- Quasinormal modes of three-dimensional rotating Hořava AdS black hole and the approach to thermal equilibrium
- Asymptotically Lifshitz spacetimes with universal horizons in dimensions
- An improved derivation of the Smarr Formula for Lorentz-breaking gravity
- Quantization of the nonprojectable 2+1D Horava theory: The second-class constraints
- Thermodynamics of 2+1 dimensional Coulomb-Like Black Holes from Non Linear Electrodynamics with a traceless energy momentum tensor
- BFV quantization of the nonprojectable 2+1 Horava theory
- The Rotating Black Hole in Renormalizable Quantum Gravity: The Three-Dimensional Hořava Gravity Case
- Extrinsic curvature in 2-dimensional Causal Dynamical Triangulation
- Motion and trajectories of photons in a three-dimensional rotating Hořava AdS black hole
- The point-particle solution and the asymptotic flatness in 2+1 Horava gravity
- Quantization of 2D Hořava gravity: non-projectable case
- Collision of particles near a three-dimensional rotating Hořava AdS black hole
- BRST symmetry and unitarity of the Horava theory
- Renormalization of the nonprojectable Horava theory
- Effective action of the Horava theory: Cancellation of divergences
- A New Extension of Hořava-Lifshitz Gravity and Curing Pathologies of the Scalar Graviton
- Holography and gravity with a dynamical aether
- Time like geodesics in three-dimensional rotating Hořava AdS black hole
- A local induced action for the noncritical string
- Asymptotic flatness and nonflat solutions in the critical 2+1 Horava theory
- Rotating Black Holes in Three-Dimensional Horava Gravity Revisited
- Batalin-Fradkin-Vilkovisky quantization of Einstein gravity with off-diagonal solutions encoding Hořava type generating functions