  We recast the system of Einstein field equations for Locally Rotationally
Symmetric spacetimes into an autonomous system of covariantly defined
geometrical variables. The analysis of this autonomous system gives all the
important global features of the maximal extension of these spacetimes. We
conclude that the dynamical system analysis can be a powerful mathematical tool
for qualitative understanding of the global structure of spacetimes
covariantly, without actually solving the field equations.
