Causality and black holes in spacetimes with a preferred foliation

TL;DR

This paper develops a framework to analyze the causal structure of spacetimes with a preferred foliation, introducing concepts like universal horizons and exploring their properties in Lorentz-violating theories such as Horava gravity.

Contribution

It formalizes the notion of universal horizons, analyzes their properties, and establishes conditions under which they are cloaked by Killing horizons in axisymmetric spacetimes.

Findings

Universal horizons are Cauchy horizons under certain evolution conditions.

A local characterization of universal horizons in stationary spacetimes is provided.

Conditions for universal horizons to be cloaked by Killing horizons are identified.

Abstract

We develop a framework that facilitates the study of the causal structure of spacetimes with a causally preferred foliation. Such spacetimes may arise as solutions of Lorentz-violating theories, e.g. Horava gravity. Our framework allows us to rigorously define concepts such as black/white holes and to formalize the notion of a `universal horizon', that has been previously introduced in the simpler setting of static and spherically symmetric geometries. We also touch upon the issue of development and prove that universal horizons are Cauchy horizons when evolution depends on boundary data or asymptotic conditions. We establish a local characterisation of universal horizons in stationary configurations. Finally, under the additional assumption of axisymmetry, we examine under which conditions these horizons are cloaked by Killing horizons, which can act like usual event horizons for low-energy excitations.