# Static self-gravitating Newtonian elastic balls

## TL;DR

This paper proves the existence of static self-gravitating elastic balls in Newtonian gravity, using dynamical systems methods and elasticity theory, covering several classical elastic material models.

## Contribution

It introduces a novel proof of existence for elastic balls under gravity, applying dynamical systems techniques to elasticity theory for spherically symmetric bodies.

## Key findings

- Existence of static elastic balls under gravity established
- Applicable to Saint Venant-Kirchhoff, John, and Hadamard materials
- Uses dynamical systems approach for proof

## Abstract

The existence of static self-gravitating Newtonian elastic balls is proved under general assumptions on the constitutive equations of the elastic material. The proof uses methods from the theory of finite-dimensional dynamical systems and the Euler formulation of elasticity theory for spherically symmetric bodies introduced recently by the authors. Examples of elastic materials covered by the results of this paper are Saint Venant-Kirchhoff, John and Hadamard materials.