A dynamical inconsistency of Horava gravity

TL;DR

This work critically analyzes the dynamics of Horava gravity in its non-projectable, asymptotically flat formulation and shows that, for generic couplings, the lapse is fixed by the Hamiltonian constraints and must vanish, eliminating nontrivial dynamics at large and small scales.The authors demonstrate that the Hamiltonian constraints are generically second-class, leaving no first-class Hamiltonian constraint to generate time reparametrizations, which they reconcile with the action's invariance by arguing that such gauge symmetry is on-shell trivial.A tractable coupling-constant model confirms that the lapse must vanish everywhere, not merely asymptotically, and they argue via continuity that this behavior extends to generic couplings, highlighting a fundamental dynamical inconsistency in Horava gravity as originally proposed.Although one could attempt to salvage the framework by adding further constraints, doing so would significantly alter the theory’s relation to general relativity and its UV motivation, casting serious doubt on the viability of the original Horava proposal.

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.