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Multi-body Spherically Symmetric Steady States of Newtonian Self-Gravitating Elastic Matter

Journal article
Authors A. Alho
Simone Calogero
Published in Communications in Mathematical Physics
Volume 371
Issue 3
Pages 975–1004
ISSN 0010-3616
Publication year 2019
Published at Department of Mathematical Sciences
Pages 975–1004
Language en
Links dx.doi.org/10.1007/s00220-019-03380...
Subject categories Mathematics

Abstract

We study the problem of static, spherically symmetric, self-gravitating elastic matter distributions in Newtonian gravity. To this purpose we first introduce a new definition of homogeneous, spherically symmetric (hyper)elastic body in Euler coordinates, i.e., in terms of matter fields defined on the current physical state of the body. We show that our definition is equivalent to the classical one existing in the literature and which is given in Lagrangian coordinates, i.e. in terms of the deformation of the body from a given reference state. After a number of well-known examples of constitutive functions of elastic bodies are re-defined in our new formulation, a detailed study of the Seth model is presented. For this type of material the existence of single and multi-body solutions is established. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

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