Electromagnetized black holes and swirling backgrounds in nonlinear electrodynamics: The ModMax case

TL;DR

This paper constructs and analyzes new black hole solutions and electromagnetic backgrounds within the nonlinear ModMax electrodynamics, revealing novel spacetime structures and representations that extend classical solutions.

Contribution

It introduces the first black hole solutions embedded in nonlinear electrodynamics and uncovers new Kerr-Schild representations and vortex-like backgrounds in Einstein-ModMax theory.

Findings

Constructed the Melvin-Bonnor electromagnetic universe in ModMax.

Presented the first black hole solutions in nonlinear electrodynamics with unique Kerr-Schild forms.

Expanded the solution spectrum with vortex-like backgrounds and a Taub-NUT spacetime in ModMax.

Abstract

This work focuses on constructing electromagnetized black holes and vortex-like backgrounds within the framework of the ModMax theory--the unique nonlinear extension of Maxwell's theory that preserves conformal symmetry and electromagnetic duality invariance. We begin by constructing the Melvin-Bonnor electromagnetic universe in ModMax through a limiting procedure that connects the spacetime of two charged accelerating black holes with that of a gravitating homogeneous electromagnetic field. Building on this result, we proceed to construct the Schwarzschild and C-metric Melvin-Bonnor black holes within the ModMax theory, representing the first black hole solutions embedded in an electromagnetic universe in the context of nonlinear electrodynamics. While the characteristics of the Melvin-Bonnor spacetime and some of its black hole extensions have been widely examined, we demonstrate for the first time that the Schwarzschild-Melvin-Bonnor configuration exhibits an unusual Kerr-Schild representation. Following this direction, we also unveil a novel Kerr-Schild construction for the spacetime of two accelerating black holes, drawing on the intrinsic relationship between the Melvin-Bonnor spacetime and the C-metric. Finally, we expand the spectrum of exact gravitational solutions within Einstein-ModMax theory by constructing a vortex-like background that coexists with the Melvin-Bonnor universe. In this process, the Taub-NUT spacetime in ModMax has played a crucial role. We present this Taub-NUT solution in a different gauge that facilitates the comparison with the Melvin-Bonnor-Swirling case.