Hamiltonian structure of Hořava gravity

William Donnelly and Ted Jacobson
Phys. Rev. D 84, 104019 – Published 8 November 2011

Abstract

The Hamiltonian formulation of Hořava 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.

  • Received 1 July 2011

DOI:https://doi.org/10.1103/PhysRevD.84.104019

© 2011 American Physical Society

Authors & Affiliations

William Donnelly* and Ted Jacobson

  • Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, Maryland, 20742-4111 USA

  • *wdonnell@umd.edu
  • jacobson@umd.edu

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Issue

Vol. 84, Iss. 10 — 15 November 2011

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