Static self-gravitating elastic bodies in Einstein gravity

Details Static self-gravitating elastic bodies in Einstein gravity Static self-gravitating elastic bodies in Einstein gravity

2006-11-20

arxiv.org/abs/gr-qc/0611108v2

Commun.PureAppl.Math.61:988-1023,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

29 pages. Updated to conform with published version, typos fixed

Scientific paper

10.1002/cpa.20230

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.

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