On weak solutions in Einstein theory and beyond

TL;DR

This paper examines the limitations of weak solutions in Einstein's theory, especially in the context of shell-crossing singularities in gravitational collapse, highlighting issues with superluminal shock waves.

Contribution

It critically analyzes the applicability of weak solutions in Einstein gravity, revealing their inadequacy for modeling shock waves in dust collapse scenarios.

Findings

Weak solutions can imply superluminal shock waves, which are physically unfeasible.

Weak solutions are ill-suited for extending spacetime beyond shell crossings in dust collapse.

The paradigm of weak solutions may not be appropriate for certain dynamical gravitational phenomena.

Abstract

In spherical symmetry, gravitational collapse of dust may give rise to the so-called shell-crossing singularities, beyond which spacetime can be extended using weak solutions to the integrated version of the equations of motion. We argue that the paradigm of weak solutions is ill-suited for dynamical extension beyond shell crossings through shock waves because it is based implicitly on an assumption that turns out to be unphysical for the shock and leads to the unwanted prospect of shock waves of dust particles moving faster than light.