  We analyze how the hypotheses of Penrose's singularity theorem (1965) are
modified by the action of disformal transformations (defined in terms of
light-like vectors) upon a given space-time metric. In particular, we
investigate the transformation of the null energy condition and the existence
of closed trapped surfaces in such scenario, in order to derive conditions upon
the background metric and the disformal vector that guarantee the validity of
Penrose's theorem for disformal metrics. Then, we explain how to apply this
technique for static and spherically symmetric space-times in general.
