The relative deformation tensor for small displacements in general relativity

By means of the world-function, an approximate formula for the relative deformation tensor of an elastic continuum in a space-time opf finite curvature is obtained. The coordinate displacements are supposed to be small with respect to the characteristic measure of the geodesic joining an arbitrary point of that continuum and a fixed point of the space-time. The formula contains all the terms up to the third order of approximation with respect to this geodesic measure, which is the basis of the approximation.