Post-Newtonian perturbed theory of elastic astronomical bodies in rotating spherical coordinates

In this paper the dynamical equations for an elastic deformable body in the firstpost-Newtonian approximation of Einstein theory of gravity are derived in rotating spherical coor-dinates.The unperturbed rotating body (the relaxed ground state) is described as uniformly rotat-ing,stationary and axisymmetric configuration in an asymptotically flat space-time manifold.Devia-tions from the equilibrium configuration are described by means of a displacement field.By makinguse of the schemes developed by Damour,Soffel and Xu,and by Carter and Quintana we calcu-late the post-Newtonian Lagrangian strain tensor and symmetric trace-free shear tensor.Consid-ering the Euler variations of Einstein’s energy-momentum conservation law,we derive the post-Newtonian energy equation and Euler equations of elastic deformable bodies in rotating sphericalcoordinates.