Electrically-Charged Lifshitz Spacetimes, and Hyperscaling Violations

TL;DR

This paper constructs new electrically-charged Lifshitz spacetimes with hyperscaling violations in higher-dimensional Einstein gravity coupled to gauge fields, including exact black hole solutions, expanding the landscape of such geometries.

Contribution

It introduces a novel class of Lifshitz solutions with hyperscaling violation sourced by Yang-Mills instantons and includes exact black hole solutions in five and four dimensions.

Findings

Constructed electrically-charged Lifshitz solutions with hyperscaling violation.

Derived exact Lifshitz black hole solutions.

Extended solutions to four-dimensional spacetime.

Abstract

Electrically-charged Lifshitz spacetimes are hard to come by. In this paper, we construct a class of such solutions in five dimensional Einstein gravity coupled to Maxwell and $SU(2)$ Yang-Mills fields. The solutions are electrically-charged under the Maxwell field, whose equation is sourced by the Yang-Mills instanton(-like) configuration living in the hyperbolic four-space of the Lifshitz spacetime. We then introduce a dilaton and construct charged and colored Lifshitz spacetimes with hyperscaling violations. We obtain a class of exact Lifshitz black holes. We also perform similar constructions in four dimensions.