Evolving wormhole geometries within nonlinear electrodynamics

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.