Spherical black holes with minimally coupled scalar cloud/hair in Einstein-Born-Infeld gravity

TL;DR

This paper explores how nonlinear electromagnetic fields in Einstein-Born-Infeld gravity influence the existence of scalar hair on black holes, revealing that increased nonlinearity can inhibit scalar cloud formation.

Contribution

It extends previous Einstein-Maxwell studies to Einstein-Born-Infeld gravity, demonstrating the impact of electromagnetic nonlinearity on scalar hair existence through numerical solutions.

Findings

Higher Born-Infeld coupling reduces the domain of scalar hair solutions.

Nonlinearity in electromagnetic fields can prevent scalar cloud formation.

Scalar hair solutions may disappear at large coupling constants.

Abstract

Previous studies showed that, in the presence of a simple and well-motivated self-interaction scalar potential, asymptotically flat and spherical black holes can carry minimally coupled and charged scalar cloud/hair in Einstein-Maxwell gravity. We extend these studies to Einstein-Born-Infeld gravity to consider the effect of nonlinearity of the electromagnetic field. Series of spherical cloudy/hairy black hole solutions are constructed numerically. Results show that increasing the Born-Infeld coupling constant $b$ will make the domain of existence of the solution shrink or even disappear when $b$ is large enough. This implies that, competing with the gravitation, nonlinearity of the electromagnetic field will make the formation of scalar cloud/hair harder or even impossible.