Evolution and spherical collapse in Einstein-Æther theory and Hořava gravity - Bhattacharyya, Jishnu; Coates, Andrew; Colombo, Mattia; Sotiriou, Thomas P. (American Physical Society, 2016)
We compare the initial value formulation of the low-energy limit of (nonprojectable) Hořava gravity to that of Einstein-æther theory when the æther is assumed to be hypersurface orthogonal at the level of the field equations. This comparison clearly highlights a crucial difference in the causal structure of the two theories at the nonperturbative level: in Hořava gravity evolution equations include an elliptic equation that is not a constraint relating initial data but needs to be imposed on each slice of the foliation. This feature is absent in Einstein-æther theory. We discuss its physical significance in Hořava gravity. We also focus on spherical symmetry, and we revisit existing collapse simulations in Einstein-æther theory. We argue that they have likely already uncovered the dynamical formation of a universal horizon and that they can act as evidence that this horizon is indeed a Cauchy horizon in Hořava gravity.