Static self-gravitating Newtonian elastic balls
Mathematical Physics
2020-08-26 v2 Earth and Planetary Astrophysics
General Relativity and Quantum Cosmology
math.MP
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.
Keywords
Cite
@article{arxiv.1907.09970,
title = {Static self-gravitating Newtonian elastic balls},
author = {Artur Alho and Simone Calogero},
journal= {arXiv preprint arXiv:1907.09970},
year = {2020}
}
Comments
30 pages, 2 figures. The order of presentation of the results and the notation have been changed considerably to improve the reading flow of the article. Some assumptions and theorems have been reformulated in a more clear way and several new remarks have been added