Static self-gravitating elastic bodies in Einstein gravity
General Relativity and Quantum Cosmology
2009-01-12 v2
Abstract
We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution constructed is a small deformation of the relaxed configuration. This result yields the first proof of existence of static solutions of the Einstein equations without symmetries.
Keywords
Cite
@article{arxiv.gr-qc/0611108,
title = {Static self-gravitating elastic bodies in Einstein gravity},
author = {Lars Andersson and Robert Beig and Bernd Schmidt},
journal= {arXiv preprint arXiv:gr-qc/0611108},
year = {2009}
}
Comments
29 pages. Updated to conform with published version, typos fixed