Gravitational collapse and topology change in spherically symmetric dynamical systems

TL;DR

This paper introduces a new numerical framework for simulating spherically symmetric gravitational collapse, capable of tracking the evolution through trapped surfaces to singularities, and explores topology change and cosmic censorship.

Contribution

A novel hyperbolic evolution scheme enabling detailed study of collapse and topology change in spherically symmetric systems, supporting the weak cosmic censorship hypothesis.

Findings

Trapped regions develop before singularities in all cases.

Ricci and Kretschmann scalars blow up at singularities, but the Einstein-Hilbert action remains finite.

Topology changes are discussed in the context of gravitational collapse.

Abstract

A new numerical framework, based on the use of a simple first order strongly hyperbolic evolution equations, is introduced and tested in case of 4-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that our numerical method is capable to follow the time evolution even after the appearance of trapped surfaces, more importantly, until the true physical singularities are reached. Using this framework, the gravitational collapse of various gravity-matter systems are investigated, with distinguished attention to the evolution in trapped regions. It is justified that in advance to the formation of these curvature singularities, trapped regions develop in all cases, thereby supporting the validity of the weak cosmic censor hypothesis of Penrose. Various upper bounds on the rate of blow-up of the Ricci and Kretschmann scalars and the Misner-Sharp mass are provided. In spite of the unboundedness of the Ricci scalar, the Einstein-Hilbert action was found to remain finite in all the investigated cases. In addition, important conceptual issues related to the phenomenon of topology changes are also discussed.