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Static self-gravitating elastic bodies in Einstein gravity

Lars Andersson·Robert Beig·Bernd Schmidt
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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.

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Lars Andersson, Robert Beig, Bernd Schmidt. 2009-01-12. Static self-gravitating elastic bodies in Einstein gravity. https://doi.org/10.1002/cpa.20230

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