Localized scalar structures around static black holes

TL;DR

This paper develops a method to find scalar field solutions around static black holes using BPS formalism, providing analytical and numerical results that demonstrate stability and conserved charges in topological black hole backgrounds.

Contribution

It introduces a novel approach combining BPS formalism with relaxed covariance to analyze scalar fields around static black holes, including analytical solutions and stability analysis.

Findings

Solutions are radially stable

Zero-mode solutions are analytically expressible

Conserved charges are identified for configurations

Abstract

In this work we address a way to capture scalar field solutions on static spacetimes by using BPS formalism and relaxing the general covariance condition. We focus on configurations where the background geometry describes topological black holes and present both analytical and numerical solutions, in addition to discussing the use of conserved charges associated to such field configurations. The obtained solutions are radially stable and the zero-mode arising from the stability equation can be written analytically.