On slowly rotating black holes and nonlinear electrodynamics

Understand

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.