Singularidades en modelos Bianchi con electrodinámica no lineal

In this contribution we shall to present a brief compilation of the Einstein field equation solutions coupled with with nonlinear electrodynamics. The metric used correspond to homogenous and anisotropic spaces Petrov type D, which has some particular cases to several conformal to Bianchi spaces, among them G₃I, G₃II, G₃III, G₃VIII, G₃IX and Kantowski-Sachs. We coupled Born-Infeld nonlinear electrodynamics with this metric [17]. Finally, an analysis of geodesic is made which indicates us that G₃ VIII is geodesically complete, but in the analysis for GII and GIX is not conclusive. Whereas for G₃I, G ₃III and the Kantowski-Sachs. it shows that are geodesically incomplete.