Analytical scalar field solutions on Lifshitz spacetimes

TL;DR

This paper derives and analyzes static scalar field solutions in Lifshitz spacetimes, demonstrating their existence and stability by breaking covariance and using a first-order formalism, with potential applications in holography.

Contribution

It introduces a method to find analytic, finite-energy scalar solutions on Lifshitz backgrounds by breaking covariance and employing a first-order approach.

Findings

Solutions exist and are stable in fixed Lifshitz backgrounds.

Finite energy solutions are obtained with radial-dependent potentials.

The approach evades Derrick's theorem on curved spacetimes.

Abstract

In this work, we investigate the existence of analytic solutions of static scalar fields on Lifshitz spacetimes. We evade Derrick's theorem on curved spacetimes by breaking general covariance and use first-order formalism to obtain solutions with finite energy related to the time-translational invariance of the background geometry along with the energy-momentum tensor of the model. We show that such solutions exist and are stable in systems where the Lifshitz background geometry is fixed and the self-interaction potential of the scalar field explicitly depends on the radial coordinate present in the metric.