Final fate of Kantowski-Sachs gravitational collapse

Abstract

Although it is not a fundamental question, to determine exact and general solutions for a given theory has advantages over a numerical integration in many specific cases. Of course, respecting the peculiarities of the problem. Revisiting the integration of the General Relativity Theory field equations for the Kantowski-Sachs spacetime, that describes a homogeneous but anisotropic universe whose spatial section has the topology of $R \times S^2$, we integrate the equations for arbitrary curvature parameter, and writing the solutions considering the process of gravitational collapse. We took the opportunity and made some comments involving some features of the model such as: energy density, shear, viscosity, and the production of gravitational waves via Petrov classification.