Separable motions for self-gravitating hyperelastic matter

TL;DR

This paper proves the existence of both expanding and collapsing separable solutions for the equations of motion in self-gravitating hyperelastic matter, including new collapsing solutions not previously known.

Contribution

It introduces the first known collapsing solutions for self-gravitating hyperelastic matter under certain constitutive assumptions.

Findings

Existence of global-in-time expanding solutions.

Construction of finite-time collapsing solutions.

New theoretical insights into self-gravitating hyperelastic matter behavior.

Abstract

In this paper, we prove the existence of separable solutions to the equations of motion for self-gravitating hyperelastic matter, under an appropriate class of constitutive assumptions on the strain-energy function. Our framework includes both global-in-time solutions which expand and also solutions which collapse to a point in finite time. Other authors have constructed expanding solutions in similar settings, but to the best of our knowledge, the collapsing solutions we construct are completely new.