2006/03/26 by CM Losert-Valiente Kroon, Kroon, CM Losert-Valiente
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Cosmology and Gravitation Theories #Elasticity and Material Modeling #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0603103
16 pages
arxiv created 2006/03/26 · openalex publication_date 2006/03/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the behaviour of a specific system of relativistic elasticity in its own gravitational field: a static, spherically symmetric shell whose wall is of arbitrary thickness consisting of hyperelastic material. We give the system of field equations and boundary conditions within the framework of the Einsteinian theory of gravity. Furthermore, we analize the situation in the Newtonian theory of gravity and obtain an existence result valid for small gravitational constants and pointwise stability by using the implicit function theorem. If one replaces the elastic material with a fluid, one finds that stable states can not exist.