Solution of a Spherically Symmetric Static Problem of General Relativity for an Elastic Solid Sphere

Valery V. Vasiliev, Leonid V. Fedorov

Abstract


The paper is concerned with the spherically symmetric static problem of the General Relativity Theory (GRT). The classical interior solution of this problem found in 1916 by K. Schwarzschild for a fluid sphere is generalized for a linear elastic isotropic solid sphere. The GRT equations are supplemented with the equation for the stresses which is similar to the compatibility equation of the theory of elasticity and is derived using the principle of minimum complementary energy for an elastic solid. Numerical analysis of the obtained solution is undertaken.


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DOI: https://doi.org/10.5539/apr.v9n6p8

Copyright (c) 2017 Valery V. Vasiliev, Leonid V. Fedorov

License URL: http://creativecommons.org/licenses/by/4.0

Applied Physics Research   ISSN 1916-9639 (Print)   ISSN 1916-9647 (Online)   Email: apr@ccsenet.org

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