Evolution and spherical collapse in Einstein-aether theory and Horava gravity

TL;DR

This paper compares the initial value formulations of Horava gravity and Einstein-aether theory, highlighting differences in causal structure and discussing implications for spherical collapse and horizon formation.

Contribution

It reveals a key difference in the evolution equations of the two theories, especially the elliptic equation in Horava gravity, and discusses its physical significance.

Findings

Horava gravity includes a non-constraint elliptic equation affecting evolution.

Existing Einstein-aether collapse simulations suggest universal horizon formation.

Universal horizons may serve as Cauchy horizons in Horava gravity.

Abstract

We compare the initial value formulation of the low-energy limit of (non-projectable) Horava gravity to that of Einstein-aether theory when the aether 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 non-perturbative level: in Horava 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-aether theory. We discuss its physical significance in Horava gravity. We also focus on spherical symmetry and we revisit existing collapse simulations in Einstein-aether 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 Horava gravity.