Ground states of self-gravitating elastic bodies

The existence of static, self-gravitating elastic bodies in the non-linear theory of elasticity is established. Equilibrium configurations of self-gravitating elastic bodies close to the reference configuration have been constructed in Beig and Schmidt (Proc R Soc Lond, 109–115, 2003) using the implicit function theorem. In contrast, the steady states considered in this article correspond to deformations of the relaxed state with no size restriction and are obtained as minimizers of the energy functional of the elastic body.