The Bonnor-Melvin magnetic 2 + 1 + p-brane solution in gravity coupled to nonlinear electrodynamics

Abstract

Abstract In this work, we present a 2 + 1 + p-brane solution in Einstein’s gravity coupled to the nonlinear electrodynamic with the Lagrangian density − F μ ν F μ ν powered by a true uniform magnetic field. The three and four-dimensional solutions coincide with the recently reported Bonnor-Melvin universe with a cosmological constant in gravity coupled with Maxwell’s linear Lagrangian in [50] and [7], respectively. The magnetic fields are produced by electric currents through coil-type wires located periodically with the discreet radii. The invariants of the spacetime are regular/constant everywhere but nonzero and proportional to Maxwell’s invariant.