A dynamical inconsistency of Hořava gravity
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 secondclass. 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 timereparametrization invariance of the action, as this invariance is shown to be a socalled “trivial gauge symmetry” in Hořava gravity, hence with no associated firstclass constraints.
 Publication:

Physical Review D
 Pub Date:
 March 2010
 DOI:
 10.1103/PhysRevD.81.064002
 arXiv:
 arXiv:0912.0399
 Bibcode:
 2010PhRvD..81f4002H
 Keywords:

 04.60.Ds;
 Canonical quantization;
 High Energy Physics  Theory
 EPrint:
 28 pages, 2 references added