POST-NEWTONIAN ESTIMATION IN RELATIVISTIC OPTICS

A post-Newtonian analysis of the theory of gravity based on the metric g(ij) (x, y) = gamma(ij)(x)+alpha/c2(1-1/n2)y(i)y(j) with the index of refraction n(x,y) is given. A generalized Lagrange space endowed with this metric is used for the study of gravitational phenomena. The index of refraction n(x,y) is expanded in integer powers of the gravitational potential U=GM/rc2 and v2/c2. It is shown that solar system tests impose a constraint on a combination of the constant alpha, the post-Newtonian parameters defining the index of refraction n(x,y), and the post-Newtonian parameter beta associated to the Riemannian metric gamma(ij)(x).