  The aim of the present work is to generalize the results given in |81] to a
generic situation for causal geodesics. It is argued that these results may be
of interest for causality issues. Recall that the presence of superluminal
signals in a generic space time $(M, g_{\mu\nu})$ does not necessarily imply
violations of the principle of causality [1]-[12]. In flat spaces, global
Lorenz invariance leads to the conclusion that closed time like curves appear
if these signals are present. In a curved space instead, there is only local
Poincare invariance, and the presence of closed causal curves may be avoided
even in presence of a superluminal mode, specially when terms violating the
strong equivalence principle appear in the action. This implies that the
standard analytic properties of the spectral components of these functions are
therefore modified and, in particular, the refraction index $n(\omega)$ is not
analytic in the upper complex $\omega$ plane. The emergence of this
singularities may also take place for non superluminal signals, due to the
breaking of global Lorenz invariance in a generic space time. In the present
work, it is argued that the homotopy properties of the Maslov index
\cite{maslov} are useful for studying how the singularities of $n(\omega)$ vary
when moving along a geodesic congruence. In addition, several conclusions
obtained in [1]-[12] are based on the Penrose limit along a null geodesic, and
they are restricted to GR with matter satisfying strong energy conditions. The
use of the Maslov index may allow a more intrinsic description of
singularities, not relying on that limit, and a generalization of these results
about non analiticity to generic gravity models with general matter content.
