Final fate of Kantowski-Sachs gravitational collapse

TL;DR

This paper derives exact solutions for Kantowski-Sachs spacetime in General Relativity, focusing on gravitational collapse, and discusses related features like energy density, shear, viscosity, and gravitational wave production.

Contribution

It provides the first integration of Einstein's equations for Kantowski-Sachs spacetime with arbitrary curvature, including analysis of collapse and physical features.

Findings

Exact solutions for arbitrary curvature parameter

Insights into gravitational collapse dynamics

Discussion of gravitational wave production

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.