Noncommutative dyonic black holes sourced by nonlinear electromagnetic fields

TL;DR

This paper develops first-order noncommutative corrections to nonlinear electrodynamics coupled with gravity, analyzing their effects on dyonic black hole solutions using perturbative methods.

Contribution

It introduces a novel framework combining noncommutative geometry with nonlinear electrodynamics in black hole solutions, employing the Seiberg-Witten map and perturbative analysis.

Findings

Derived first-order noncommutative corrections to black hole metrics and gauge potentials.

Applied the framework to several nonlinear electrodynamics theories, obtaining explicit corrections.

Demonstrated the impact of noncommutativity on black hole properties in a perturbative regime.

Abstract

We introduce the first-order noncommutative (NC) corrections to the general nonlinear electrodynamics (NLE) Lagrangian depending on two electromagnetic invariants. The NC deformation of Einstein-NLE theory is implemented using the $\partial_t\wedge\partial_\varphi$ Drinfel'd twist and the NC effects are encoded in the matter sector through the Seiberg-Witten map. The resulting equations of motion reflect two distinct sources of nonlinearity in this framework; one arising from replacing Maxwell's electrodynamics with its nonlinear modifications and another from the NC deformations. Assuming a general form of static, spherically symmetric dyonic black hole as a seed solution in the commutative limit, we solve the equations of motion perturbatively to the first order in the NC parameter $a$. Finally, we evaluate the obtained corrections to the metric tensor and gauge potential for several prominent NLE theories.