General-relativistic theory of elastic deformable astronomical bodies - art. no. 043002

This paper deals with general perturbations of astronomical bodies in the f irst post-Newtonian approximation of Einstein's theory of gravity. The form alism starts with a description of some stationary axisymmetric configurati on in an asymptotically flat space-time manifold. General perturbations of this configuration are first treated within the Carter-Quintana framework w here the bodies are assumed to be composed of some perfectly elastic materi al. Deviations from the equilibrium configuration are described by means of some displacement field as in the local theory fur the global motion of Ea rth in space. As central results the post-Newtonian perturbation equations for the displacement field, the perturbed field, and local matter variables are presented. Especially for further discussions of global geodynamics (p recession, nutation, polar motion, length of day variations) in the framewo rk of general relativity the results presented here might serve as a new st arting point. We also derive the perturbed Euler equation for vanishing she ar stresses, i.e., for a fluid body, by means of a linearization procedure around the equilibrium state. After taking the Eulerian variations of the l ocal matter variables in terms of the displacement field from the Carter-Qu intana framework the two methods are found to produce the same results.