ModMax Black Holes in 4-Dimensional Einstein-Gauss-Bonnet Gravity

TL;DR

This paper derives and analyzes exact charged black hole solutions in 4D Einstein-Gauss-Bonnet gravity coupled with ModMax nonlinear electrodynamics, revealing unique thermodynamic and stability properties with potential observational implications.

Contribution

It provides the first exact static, spherically symmetric black hole solutions in 4D Einstein-Gauss-Bonnet gravity with ModMax electrodynamics, exploring their thermodynamics, particle orbits, and quasinormal modes.

Findings

Black holes exhibit a minimum mass and stable remnants.

Higher curvature and nonlinear effects alter spacetime and horizon structure.

Quasinormal modes depend on Gauss-Bonnet and ModMax parameters, confirming stability.

Abstract

In this paper, we study charged black hole solutions in 4-dimensional Einstein-Gauss-Bonnet gravity combined with ModMax nonlinear electrodynamics. This is a conformally invariant extension of Maxwell theory that effectively describes nonlinear electromagnetic phenomena. Within the regularized 4-dimensional Gauss-Bonnet framework, we derive an exact static and spherically symmetric black hole solution that is sourced by a purely electric ModMax field. We explore how higher curvature corrections and nonlinear electromagnetic effects change the spacetime geometry, horizon structure, and energy content of the black hole. We examine the thermodynamic properties in detail, revealing a minimum mass and stable black hole remnants. These findings might be significant in scenarios involving dark-sector compact objects or evaporation endpoints beyond standard general relativity. We also investigate the motion of massive particles, discussing the characteristics of circular orbits and the innermost stable circular orbit, highlighting differences from the Maxwell case. Additionally, we analyze the quasinormal modes of a massive scalar field using WKB methods with Pad\'{e} approximants and the P\"{o}schl-Teller approximation. We explore how the quasinormal spectrum depends on the Gauss-Bonnet coupling, the ModMax parameter, and the scalar field mass. Our results confirm the linear stability of the black hole and offer potential observational signatures of dark-sector inspired modifications of gravity and electrodynamics.