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In this work we explore the possible existence of static, sphericallysymmetric and stationary, axisymmetric traversable wormholes coupled tononlinear electrodynamics. Considering static and spherically symmetric (2+1)and (3+1)-dimensional wormhole spacetimes, we verify the presence of an eventhorizon and the non-violation of the null energy condition at the throat. Forthe former spacetime, the principle of finiteness is imposed, in order toobtain regular physical fields at the throat. Next, we analyze the(2+1)-dimensional stationary and axisymmetric wormhole, and also verify thepresence of an event horizon, rendering the geometry non-traversable.Relatively to the (3+1)-dimensional stationary and axisymmetric wormholegeometry, we find that the field equations impose specific conditions that areincompatible with the properties of wormholes. Thus, we prove the non-existenceof the general class of traversable wormhole solutions, outlined above, withinthe context of nonlinear electrodynamics.Comment: 9 pages, Revtex4. V2: major change in title; considerable additions  in the Introduction and in the rotating solution, no physics changes;  correction of a reference, one reference added; now 10 pages. This version to  appear in Classical and Quantum Gravit

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