Separable motions for self-gravitating hyperelastic matter

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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.

Keywords

hyperelastic matter / self-gravitation / separable/homologous solutions / strain energy / solid vacuum boundary conditions

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