A dynamical inconsistency of Hořava gravity

Marc Henneaux, Axel Kleinschmidt, and Gustavo Lucena Gómez
Phys. Rev. D 81, 064002 – Published 3 March 2010

Abstract

The dynamical consistency of the nonprojectable version of Hořava gravity is investigated by focusing on the asymptotically flat case. It is argued that for generic solutions of the constraint equations the lapse must vanish asymptotically. We then consider particular values of the coupling constants for which the equations are tractable and in that case we prove that the lapse must vanish everywhere—and not only at infinity. Put differently, the Hamiltonian constraints are generically all second-class. We then argue that the same feature holds for generic values of the couplings, thus revealing a physical inconsistency of the theory. In order to cure this pathology, one might want to introduce further constraints but the resulting theory would then lose much of the appeal of the original proposal by Hořava. We also show that there is no contradiction with the time-reparametrization invariance of the action, as this invariance is shown to be a so-called “trivial gauge symmetry” in Hořava gravity, hence with no associated first-class constraints.

  • Received 10 December 2009

DOI:https://doi.org/10.1103/PhysRevD.81.064002

©2010 American Physical Society

Authors & Affiliations

Marc Henneaux1,2,*, Axel Kleinschmidt1,†, and Gustavo Lucena Gómez1,‡

  • 1Université Libre de Bruxelles and International Solvay Institutes, ULB-Campus Plaine CP231, 1050 Brussels, Belgium
  • 2Centro de Estudios Científicos (CECS), Casilla 1469, Valdivia, Chile

  • *henneaux@ulb.ac.be
  • axel.kleinschmidt@ulb.ac.be
  • glucenag@ulb.ac.be

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Issue

Vol. 81, Iss. 6 — 15 March 2010

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