Static elastic deformations in general relativity

Abstract

We present a new approach to the theory of static deformations of elastic test bodies in general relativity based on a generalization of the concept of frame of reference which we identify with the concept of quo-harmonic congruence. We argue on the basis of this new approach that weak gravitational plane waves do not couple to elastic bodies and therefore the latter, whatever their shape, are not suitable antennas to detect them.