Black Holes and Thunderbolt Singularities with Lifshitz Scaling Terms

TL;DR

This paper explores black hole solutions in Einstein-aether theory with Lifshitz scaling modifications, revealing regular horizons or thunderbolt singularities depending on the ultraviolet terms included.

Contribution

It introduces new black hole solutions with Lifshitz scaling terms in Einstein-aether theory, highlighting the effects of different ultraviolet modifications on horizon and singularity structure.

Findings

Existence of a two-parameter family of black holes with regular universal horizons.

Identification of thunderbolt singularities when Ricci curvature squared terms are included.

Dependence of horizon regularity on ultraviolet modification terms.

Abstract

We study a static, spherically symmetric and asymptotic flat spacetime, assuming the hypersurface orthogonal Einstein-aether theory with an ultraviolet modification motivated by the Horava-Lifshitz theory, which is composed of the $z=2$ Lifshitz scaling terms such as scalar combinations of a three-Ricci curvature and the acceleration of the aether field. For the case with the quartic term of the acceleration of the aether field, we obtain a two-parameter family of black hole solutions, which possess a regular universal horizon. While, if three-Ricci curvature squared term is joined in ultraviolet modification, we find a solution with a thunderbolt singularity such that the universal horizon turns to be a spacelike singularity.