Scalar fields and Lifshitz black holes from Derrick's theorem evasion

TL;DR

This paper explores scalar fields in Lifshitz spacetimes, demonstrating how evading Derrick's theorem enables the construction of Lifshitz black hole solutions with backreaction effects.

Contribution

It introduces a novel method to evade Derrick's theorem in Lifshitz backgrounds, leading to new black hole solutions with scalar fields and backreaction.

Findings

Found Lifshitz black hole solutions with scalar fields

Demonstrated evasion of Derrick's theorem in this context

Established a first-order formalism for localized solutions

Abstract

We study classical scalar fields in asymptotically Lifshitz spacetimes. By evading Derrick's theorem requiring the scalar potential to explicitly depend on the background coordinates, we induce a diffeomorphism invariance breaking and settle a first-order formalism to find spatially localized solutions in the probe field limit. By inserting a backreaction equipped with a cosmological constant and a Maxwell term coupled to a dielectric function in the model, we find a Lifshitz black hole solution.