A regular universe filled with uniform electric and magnetic field

Abstract

Starting with a generic nonlinear electrodynamic Lagrangian L=L(F,G) we show that the linear Maxwell Lagrangian belongs to a class of generic nonlinear electrodynamic Lagrangian which admits conformally flat Bertotti-Robinson solution in 3+1- dimensions. The model is conformal invariant with a zero-trace energy-momentum tensor. Furthermore, the electric field of a point charge is found to be the same as the linear Maxwell with or without the presence of a magnetic monopole. The causality and unitarity principles are also studied which impose constraints on the actual form of the Lagrangian density.