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4.3 Elasticity theory

There is an extensive literature on mathematical elasticity theory but the mathematics of self-gravitating elastic bodies seems to have been largely neglected. An existence theorem for spherically symmetric elastic bodies in general relativity was mentioned in Section 3.1. More recently, Beig and Schmidt [42] proved an existence theorem for static elastic bodies subject to Newtonian gravity, which need not be spherically symmetric. This was extended to rotating bodies and special relativity in [44].


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