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Global structure of Black Holes via dynamical system

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.