Global structure of Black Holes via dynamical system

TL;DR

This paper reformulates Einstein's equations for certain symmetric spacetimes into an autonomous dynamical system, enabling a qualitative analysis of their global structure without explicit solutions.

Contribution

It introduces a covariant dynamical system approach to analyze the global features of Locally Rotationally Symmetric spacetimes.

Findings

Reveals global features of spacetime extensions

Provides a covariant method for qualitative analysis

Avoids explicit solutions of Einstein's equations

Abstract

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.