On slowly rotating black holes and nonlinear electrodynamics

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 γ 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 γ provides the Lense–Thirring line element associated to any non-linear electrodynamics; the Kerr–Newman metric for slow rotation arises when γ is not vanishing, a feature that emphasises the unique role played by Maxwell's electrodynamics. (paper)