Eur. Phys. J. Plus (2021) 136: 285
https://doi.org/10.1140/epjp/s13360-021-01264-8

Regular Article

A regular universe filled with uniform electric and magnetic field

Department of Physics, Faculty of Arts and Sciences, Eastern Mediterranean University, North Cyprus via Mersin 10, Famagusta, Turkey

^a habib.mazhari@emu.edu.tr

Received: 8 August 2020
Accepted: 21 February 2021
Published online: 3 March 2021

Abstract

Starting with a generic nonlinear electrodynamic Lagrangian $\mathcal{L}=\mathcal{L}(\mathcal{F},\mathcal{G})$, 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.