Static, Self-Gravitating Elastic Bodies

TL;DR

This paper proves an existence theorem for static, self-gravitating elastic bodies within Newtonian gravity, accommodating arbitrary shapes for small bodies made of elastic material.

Contribution

It provides the first existence proof for such bodies with arbitrary shapes in the Newtonian framework.

Findings

Existence of static, self-gravitating elastic bodies established.

Applicable to bodies of arbitrary shape, provided they are sufficiently small.

Advances understanding of equilibrium configurations in elastic self-gravitating systems.

Abstract

There is proved an existence theorem, in the Newtonian theory, for static, self-gravitating bodies composed of elastic material. The theorem covers the case where these bodies are small, but allows them to have arbitrary shape.