A dynamical inconsistency of Horava gravity

By M. Henneaux, Axel Kleinschmidt, Gustavo Lucena G'omez. 2009

142 citations recorded by the source corpus.

The dynamical consistency of the nonprojectable version of Ho\ifmmode \check{r}\else \v{r}\fi{}ava 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\char22{}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 Ho\ifmmode \check{r}\else \v{r}\fi{}ava. 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 Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity, hence with no associated first-class constraints.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/066622f61f936dd1b8b0d6344cf44041e628fd1a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

General covariance in quantum gravity at a Lifshitz point (2010, background): “One interesting exception has been found in the infrared limit [23] (see also [19, 24]): Adding π ≡ gijπ as another constraint closes the algebra, turning π and H0 into a pair of second-class constraints.”
Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry (2015, unknown): “[38, 39, 40, 41, 42, 43, 44, 45].”
Models of non-relativistic quantum gravity: the good, the bad and the healthy (2010, background): “This is precisely what happens in the original realization [1] of Hoyrava’s proposal where the behavior of the khronon turns out to be problematic [13, 22, 23] (see also [24, 25 ] for the discussion of pathologies in a restricted version of the model).”
Modified Gravity and Cosmology (2011, background): “This manifests itself through the lapse function vanishing asymptotically for generic solutions to the constraint equations [603].”