Hamiltonian structure of Horava gravity

Abstract

The Hamiltonian formulation of Horava gravity is derived. In a closed universe the Hamiltonian is a sum of generators of gauge symmetries, the foliation-preserving diffeomorphisms, and vanishes on shell. The scalar constraint is second class, except for a global, first-class part that generates time reparametrizations. A reduced phase space formulation is given in which the local part of the scalar constraint is solved formally for the lapse as a function of the 3 metric and its conjugate momentum. In the infrared limit the scalar constraint is linear in the square root of the lapse. For asymptotically flat boundary conditions the Hamiltonian is a sum of bulk constraints plus a boundary term that gives the total energy. This energy expression is identical to the one for Einstein-aether theory which, for static spherically symmetric solutions, is the usual Arnowitt-Deser-Misner energy of general relativity with a rescaled Newton constant.

8 pages, no figures. v2: added references, corrected minor typographical errors. v3: matches PRD version

References in corpus (8)

• Quantum Gravity at a Lifshitz Point
• On the Extra Mode and Inconsistency of Horava Gravity
• Black holes in Einstein-aether and Horava-Lifshitz gravity
• Horava-Lifshitz gravity: a status report
• Gravitational Radiation in Horava Gravity
• Consistency of the Hamiltonian formulation of the lowest-order effective action of the complete Horava theory
• Cosmic alignment of the aether
• Closure of the algebra of constraints for a nonprojectable Hořava model

Cited by in corpus (56)

• Hořava Gravity at a Lifshitz Point: A Progress Report
• A positive energy theorem for Einstein-aether and Hořava gravity
• Consistency of the Hamiltonian formulation of the lowest-order effective action of the complete Horava theory
• Consistent Horava gravity without extra modes and equivalent to general relativity at the linearized level
• Hamiltonian analysis of curvature-squared gravity with or without conformal invariance
• Causality and black holes in spacetimes with a preferred foliation
• 3+1 Formulation of the Standard-Model Extension Gravity Sector
• The constraints of post-quantum classical gravity
• Cancellation of divergences in the nonprojectable Horava theory
• Evolution and spherical collapse in Einstein-aether theory and Horava gravity
• Initial value constraints with tensor matter
• More on "Little Lambda" in Hořava-Lifshitz Gravity
• Quantization of the Horava theory at the kinetic-conformal point
• Non-perturbative analysis of the constraints and the positivity of the energy of the complete Horava theory
• On the first law of black holes with a universal horizon
• Wormholes and naked singularities in the complete Horava theory
• An improved derivation of the Smarr Formula for Lorentz-breaking gravity
• Quantization of the nonprojectable 2+1D Horava theory: The second-class constraints
• Linearized gravity with matter time
• The anisotropic coupling of gravity and electromagnetism in Hořava-Lifshitz theory
• Non-Projectable Horava-Lifshitz Gravity without Unwanted Scalar Graviton
• BFV quantization of the nonprojectable 2+1 Horava theory
• Black Holes in Ultraviolet-Complete Horava Gravity
• Pure electromagnetic-gravitational interaction in Hořava-Lifshitz theory at the kinetic conformal point
• Chaos, Dirac observables and constraint quantization
• Black Holes and Thunderbolt Singularities with Lifshitz Scaling Terms
• The Hamiltonian Dynamics of Horava Gravity
• The point-particle solution and the asymptotic flatness in 2+1 Horava gravity
• Wormholes in Horava gravity with cosmological constant
• Quantization of 2D Hořava gravity: non-projectable case
• BRST symmetry and unitarity of the Horava theory
• Quantum Lagrangian of the Horava theory and its nonlocalities
• Renormalization of the nonprojectable Horava theory
• Spherically symmetric solutions of the $\lambda$-R model
• Effective action of the Horava theory: Cancellation of divergences
• Restricted f(R) Gravity and Its Cosmological Implications
• Well-posed evolution of field theories with anisotropic scaling: the Lifshitz scalar field in a black hole space-time
• Higher derivative gravity with spontaneous symmetry breaking: Hamiltonian analysis of new covariant renormalizable gravity
• Einstein-aether models III: conformally static metrics, perfect fluid and scalar fields
• Constraints on Hořava-Lifshitz gravity from GRB 170817A
• Black hole horizons at the extremal limit in Lorentz-violating gravity
• Propagation of anisotropic gravitational and electromagnetic waves at very high energies
• Quantum Cauchy Surfaces in Canonical Quantum Gravity
• On the viability of minimal Hořava gravity
• Hamiltonian Analysis of Mixed Derivative Horava-Lifshitz Gravity
• Universal horizons and Hawking radiation in nonprojectable 2d Hořava gravity coupled with a non-relativistic scalar field
• Two Dimensional F(R) Horava-Lifshitz Gravity
• Quantization of the anisotropic conformal Horava theory
• Asymptotic flatness and nonflat solutions in the critical 2+1 Horava theory
• Quantizing non-projectable Hořava gravity with Lagrangian path integral
• Spontaneous Symmetry Breaking and Landau Phase Transition in Horava Gravity
• Cosmological Perturbations in Restricted f(R)-Gravity
• Phenomenologically viable gravitational theory based on a preferred foliation without extra modes
• Rotating Black Holes in Three-Dimensional Horava Gravity Revisited
• Curvature vs degrees of freedom: The case of the critical 2+1 Horava theory
• Endeavours in Discrete Lorentzian Geometry; A thesis in five papers