### 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].