Evolving wormhole geometries within nonlinear electrodynamics

TL;DR

This paper investigates evolving wormhole solutions in (2+1) and (3+1) dimensions within nonlinear electrodynamics, finding regular solutions only under specific conditions and highlighting limitations due to singularities.

Contribution

It introduces evolving wormhole models conformally related to static geometries in nonlinear electrodynamics, analyzing their physical viability and singularity properties.

Findings

(3+1)-dimensional wormholes are contracting and satisfy weak energy condition

Electric fields cause singularities at the throat, while magnetic fields do not

(2+1)-dimensional wormholes are singular at the throat, limiting their physical acceptability

Abstract

In this work, we explore the possibility of evolving (2+1) and (3+1)-dimensional wormhole spacetimes, conformally related to the respective static geometries, within the context of nonlinear electrodynamics. For the (3+1)-dimensional spacetime, it is found that the Einstein field equation imposes a contracting wormhole solution and the obedience of the weak energy condition. Nevertheless, in the presence of an electric field, the latter presents a singularity at the throat, however, for a pure magnetic field the solution is regular. For the (2+1)-dimensional case, it is also found that the physical fields are singular at the throat. Thus, taking into account the principle of finiteness, which states that a satisfactory theory should avoid physical quantities becoming infinite, one may rule out evolving (3+1)-dimensional wormhole solutions, in the presence of an electric field, and the (2+1)-dimensional case coupled to nonlinear electrodynamics.