Structure equations of a slowly rotating, fully relativistic solid star

General-relativistic elasticity theory is applied to the derivation of the structure equations for a relativistic rotating solid star with a spherically relaxable structure. The analysis is carried out to third order in the angular velocity. In this way one obtains the deformation of the star and its stress field, the change in gravitational mass, and the change in the moment of inertia. This last quantity is the key parameter needed for the application of the general-relativistic starquake theory of neutron stars