Nonlinear electrodynamics and regular black holes

Abstract

In this work, an exact regular black hole solution in General Relativity is presented. The source is a nonlinear electromagnetic field with the algebraic structure $$ T^{0}_{0}=T^{1}_{1} $$ for the energy–momentum tensor, partially satisfying the weak energy condition but not the strong energy condition. In the weak field limit, the EM field behaves like the Maxwell field. The solution corresponds to a charged black hole with $$q\le 0.77$$ $$\hbox {m}$$ . The metric, the curvature invariants, and the electric field are regular everywhere. The BH is stable against small perturbations of spacetime and using the Weinhold metric, geometrothermodynamical stability has been investigated. Finally we investigate the idea that the observable universe lives inside a regular black hole. We argue that this picture might provide a viable description of universe.