AdS–dS stationary rotating black hole exact solution within Einstein-nonlinear electrodynamics

Abstract

In this report the exact rotating charged black hole solution to the Einstein–nonlinear electrodynamics theory with a cosmological constant is presented. This black hole is equipped with mass, rotation parameter, electric and magnetic charges, cosmological constant Λ, and three parameters due to the nonlinear electrodynamics: β is associated to the potential vectors Aμ and ⋆Pμ, and two constants, F0 and G0, due to the presence of the invariants F and G in the Lagrangian L(F(xμ),G(xμ)). This solution is of Petrov type D, characterized by the Weyl tensor eigenvalue Ψ2, the traceless Ricci tensor eigenvalue S=2Φ(11), and the scalar curvature R; it allows for event horizons, exhibits a ring singularity and fulfils the energy conditions. Its Maxwell limit is the de Sitter-Anti–de Sitter–Kerr–Newman black hole solution.