Elastodynamics in a laterally heterogeneous, self-gravitating body

We consider the question of whether the self-gravitation problem requires the use of finite strain theory. After concluding that ordinary linearized elasticity theory is applicable, a variational formulation for a laterally heterogenous self-gravitating body is presented in a computationally tractable form. After errors in the derivation of previous theoretical results are corrected, they are shown to agree with the results derived in the present paper.