Static self-gravitating elastic bodies in Einstein gravity
arXiv:gr-qc/0611108 · doi:10.1002/cpa.20230
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.
29 pages. Updated to conform with published version, typos fixed
References in corpus (6)
- Well posedness for the motion of a compressible liquid with free surface boundary
- Relativistic Elasticity
- Weakly decaying asymptotically flat static and stationary solutions to the Einstein equations
- Static, Self-Gravitating Elastic Bodies
- Relativistic Elastostatics I: Bodies in Rigid Rotation
- On the motion of a compact elastic body
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