On slowly rotating black holes and nonlinear electrodynamics

TL;DR

This paper explores solutions for slowly rotating black holes within nonlinear electrodynamics, revealing how different rotation schemes depend on a parameter and how Maxwell's electrodynamics uniquely relates to the Kerr-Newman metric.

Contribution

It introduces a new class of solutions for slowly rotating black holes coupled to nonlinear electrodynamics, highlighting the role of a parameter in defining rotation schemes.

Findings

Different rotation schemes depend on a parameter $oldsymbol{\gamma}$.

Vanishing $oldsymbol{\gamma}$ yields the Lense-Thirring metric.

Non-zero $oldsymbol{\gamma}$ leads to Kerr-Newman-like solutions.

Abstract

We discuss the solution to Einstein's equations for a Lense-Thirring inspired metric describing a slowly rotating black hole coupled to nonlinear electrodynamics. We show that different schemes of rotation for the black hole exist; they depend on a parameter $\gamma$ defining the dependence of the metric on the polar angle. The fulfilment of the complete set of gravitational field equations and conservation laws implies constraints on this parameter and the metric functions. The vanishing of $\gamma$ provides the Lense-Thirring line element associated to any non-linear electrodynamics; the Kerr-Newman metric for slow rotation arises when $\gamma$ is not vanishing, a feature that emphasises the unique role played by Maxwell's electrodynamics.