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Journal Article

Static self-gravitating elastic bodies in Einstein gravity

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Andersson,  Lars
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Beig,  Robert
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Schmidt,  Bernd G.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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cpa.20230.pdf
(Publisher version), 290KB

0611108.pdf
(Preprint), 360KB

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Citation

Andersson, L., Beig, R., & Schmidt, B. G. (2008). Static self-gravitating elastic bodies in Einstein gravity. Communications on Pure and Applied Mathematics, 61: 1023. 988. doi:10.1002/cpa.20230.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-470A-3
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.