Static Solutions of the Einstein Equations for Spherically Symmetric Elastic Bodies

Details Static Solutions of the Einstein Equations for Spherically Symmetric Elastic Bodies Static Solutions of the Einstein Equations for Spherically Symmetric Elastic Bodies

1998-10-04

arxiv.org/abs/gr-qc/9810010v1

Gen.Rel.Grav. 32 (2000) 235-252

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages, TeX

Scientific paper

The paper is concerned with the Einstein equations for a spherically symmetric static distribution of anisotropic matter. The equations are cast into a system of Fuchsian type ODE for certain scalar invariants of the strain. And then the existence and regularity of this ODE is studied under general constitutive relation. In the case the constitutive relation is given by a quadratic form of strain, it is also shown that the solutions stay regular up to the boundary of the material ball.

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