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Communications in Mathematical Physics

, Volume 371, Issue 3, pp 975–1004 | Cite as

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

  • A. AlhoEmail author
  • S. Calogero
Article

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.

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Notes

Acknowledgements

A. A. is supported by the project (GPSEinstein) PTDC/MAT-ANA/1275/2014, by CAMGSD, Instituto Superior Técnico, through FCT/Portugal UID/MAT/04459/2013, and by the FCT Grant No. SFRH/BPD/85194/2012. Furthermore, A. A. thanks the Department of Mathematics at Chalmers University, Sweden, for the very kind hospitality.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal
  2. 2.Department of Mathematical SciencesChalmers University of Technology, University of GothenburgGothenburgSweden

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