A dynamical inconsistency of Horava gravity

TL;DR

This paper analyzes the dynamical consistency of non-projectable Horava gravity, revealing that the theory faces a fundamental inconsistency where the lapse function must vanish, challenging its physical viability.

Contribution

It demonstrates that the Hamiltonian constraints in non-projectable Horava gravity are generically second-class, leading to a physical inconsistency in the theory.

Findings

Lapse function must vanish asymptotically for generic solutions.

For certain coupling constants, the lapse vanishes everywhere.

The constraints are generically second-class, indicating inconsistency.

Abstract

The dynamical consistency of the non-projectable version of Horava 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 Horava. 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 Horava gravity, hence with no associated first-class constraints.