Non-existence of static, spherically symmetric and stationary, axisymmetric traversable wormholes coupled to nonlinear electrodynamics

In this work we explore the possible existence of static, spherically symmetric and stationary, axisymmetric traversable wormholes coupled to nonlinear electrodynamics. Considering static and spherically symmetric (2+1) and (3+1)-dimensional wormhole spacetimes, we verify the presence of an event horizon and the non-violation of the null energy condition at the throat. For the former spacetime, the principle of finiteness is imposed, in order to obtain regular physical fields at the throat. Next, we analyze the (2+1)-dimensional stationary and axisymmetric wormhole, and also verify the presence of an event horizon, rendering the geometry non-traversable. Relatively to the (3+1)-dimensional stationary and axisymmetric wormhole geometry, we find that the field equations impose specific conditions that are incompatible with the properties of wormholes. Thus, we prove the non-existence of the general class of traversable wormhole solutions, outlined above, within the context of nonlinear electrodynamics.