Magnetized dynamical black holes

TL;DR

This paper presents a new exact solution describing a dynamical black hole in a time-dependent electromagnetic field, incorporating realistic features like a cosmological background and non-perturbative backreaction.

Contribution

It introduces a novel analytical model of a dynamical black hole with scalar and electromagnetic fields, extending previous solutions to include time dependence and complex asymptotic structures.

Findings

The solution features a dynamical horizon with rich geometric properties.

Time dependence can potentially cloak singularities that are naked in stationary limits.

The model has implications for primordial black holes and astrophysical phenomena.

Abstract

We construct a novel exact solution of the Einstein-scalar-Maxwell equations describing a dynamical black hole immersed in an external, time-dependent electromagnetic field. Motivated by the need for more realistic analytical black hole models, our construction incorporates two key ingredients often neglected in exact solutions: a fully dynamical cosmological background and the non-perturbative backreaction of external electromagnetic fields. The compact object is obtained by dressing a Schwarzschild black hole with a radially and temporally dependent scalar field, yielding a time-dependent generalization of the Fisher-Janis-Newman-Winicour solution within the Fonarev framework. The external electromagnetic field is generated via a Lie point symmetry of the Einstein-scalar-Maxwell system, which exports the effect of a Harrison transformation to dynamical settings provided a spacelike Killing vector is present. The resulting spacetime combines a spherically symmetric dynamical horizon with an axisymmetric electromagnetic field and exhibits a rich asymptotic structure mixing Friedmann-Lema\^itre-Robertson-Walker and Levi-Civita geometries. We show that the time dependence of the configuration plays a crucial role in potentially cloaking curvature singularities, which would otherwise be generically naked in the stationary limit. We analyze the geometric and physical properties of the solution, including its asymptotic behavior, algebraic classification, and the structure of trapped surfaces defining the dynamical horizon. Possible implications for primordial black holes and some astrophysical applications, as well as extensions to higher dimensions, are also discussed.