Multibody Spherically Symmetric Steady States of Newtonian SelfGravitating Elastic Matter
Abstract
We study the problem of static, spherically symmetric, selfgravitating 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 wellknown examples of constitutive functions of elastic bodies are redefined in our new formulation, a detailed study of the Seth model is presented. For this type of material the existence of single and multibody solutions is established.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 November 2019
 DOI:
 10.1007/s00220019033800
 arXiv:
 arXiv:1807.03062
 Bibcode:
 2019CMaPh.371..975A
 Keywords:

 Mathematical Physics;
 General Relativity and Quantum Cosmology
 EPrint:
 33 pages, 1 figure. v2 matches final published version