Hamiltonian structure of Horava gravity

TL;DR

This paper derives the Hamiltonian formulation of Horava gravity, revealing its gauge symmetries, constraints, and energy expression, and compares it to Einstein-aether theory in the infrared limit.

Contribution

It provides a detailed Hamiltonian analysis of Horava gravity, including the structure of constraints and the energy expression, linking it to Einstein-aether theory.

Findings

Hamiltonian is a sum of gauge generators and vanishes on shell.

Scalar constraint is second class except for a global first-class part.

Energy expression matches ADM energy in the IR limit.

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.