Scalar Hairy Black Holes in the presence of Nonlinear Electrodynamics

TL;DR

This paper investigates how scalar fields affect nonlinear electrodynamics black hole solutions, revealing that certain horizon regularity issues persist even with nonlinear electromagnetic sources, through both analytic and test field analyses.

Contribution

It provides the first detailed analysis of scalar fields in nonlinear electrodynamics black hole spacetimes, especially focusing on the Square Root Lagrangian model, and examines horizon regularity.

Findings

Scalar fields do not improve horizon regularity in these spacetimes.

Nonlinear Electrodynamics does not eliminate scalar field-induced singularities.

Test field analysis confirms the persistence of horizon issues beyond spherical symmetry.

Abstract

We study influence of scalar fields on Nonlinear Electrodynamics spacetimes. The investigation is carried out using both test and gravitating scalar fields. After revisiting Einstein-Maxwell scalar field solutions we focus on analytic investigation of Nonlinear Electrodynamics scalar field spacetimes, especially Square Root Lagrangian model. The main motivation being to understand whether certain specific signatures of scalar fields are preserved when Nonlinear Electrodynamics as an additional source is considered. We show that the regularity of horizon which is spoiled by scalar field in spherically symmetric static scalar-vacuum spacetimes is not improved by including Nonlinear Electrodynamics or other sources satisfying certain condition. We confirm these findings using test scalar field that enables us to go beyond spherical symmetry.