Sectors of spherical homothetic collapse

TL;DR

This paper analyzes the gravitational collapse of spherically symmetric thick shells with homothetic symmetry, identifying conditions under which naked singularities can form from nearly trivial initial data, highlighting their stability.

Contribution

It characterizes the global structure of homothetic collapse spacetimes, showing the existence and stability of naked singularities under certain energy conditions.

Findings

Naked singularities are stable and can form from small deviations in initial data.

The metric depends on a single function constrained by energy conditions.

Certain classes of solutions lead to naked singularities, not censored by horizons.

Abstract

A study is undertaken of the gravitational collapse of spherically symmetric thick shells admitting a homothetic Killing vector field under the assumption that the energy momentum tensor corresponds to the absence of a pure outgoing component of field. The energy-momentum tensor is not specified beyond this, but is assumed to satisfy the strong and dominant energy conditions. The metric tensor depends on only one function of the similarity variable and the energy conditions identify a class of functions ${\cal F}$ to which the metric function may belong. The possible global structure of such space-times is determined, with particular attention being paid to singularities and their temporal nature (naked or censored). It is shown that there are open subsets of ${\cal F}$ which correspond to naked singularities; in this sense, such singularities are stable. Furthermore, it is shown that these singularities can arise from regular (continuous), asymptotically flat initial data which deviate from the trivial data by an arbitrarily small amount.