Quasilocal approach to general universal horizons

TL;DR

This paper introduces a quasilocal definition of universal horizons in theories of gravity with preferred foliation, analyzes their properties in cosmological models, and studies their formation in spherical symmetry within Horava-Lifshitz theory.

Contribution

It proposes a new quasilocal formalism for universal horizons, independent of symmetries, and applies it to analyze horizon formation and absence in FLRW cosmologies.

Findings

Universal horizons are absent in FLRW models for any scale factor.

Quasilocal universal horizons are confined to trapped regions.

Horizon formation can be non-smooth under certain conditions in Horava-Lifshitz gravity.

Abstract

Theories of gravity with a preferred foliation usually display arbitrarily fast signal propagation, changing the black hole definition. A new inescapable barrier, the universal horizon, has been defined and many static and spherically symmetric examples have been studied in the literature. Here, we translate the usual definition of the universal horizon in terms of an optical scalar built with the preferred flow defined by the preferred spacetime foliation. The new expression has the advantages of being of quasilocal nature and independent of specific spacetime symmetries in order to be well defined. Therefore, we propose it as a definition for general quasilocal universal horizons. Using the new formalism we show that there are no universal analog of cosmological horizons for FLRW models for any scale factor function, and we also state that quasilocal universal horizons are restricted to trapped regions of the spacetime. Using the evolution equation, we analyze the formation of universal horizons under a truncated Horava-Lifshitz theory, in spherical symmetry, showing the existence of regions in parameter space where the universal horizon formation cannot be smooth from the center, under some physically reasonable assumptions. We conclude with our view on the next steps for the understanding of black holes in nonrelativistic gravity theories.