2-post-Newtonian approximation of a nonstationary spherically symmetric star in flat space-time theory of gravitation

Abstract

Starting from a previously stated theory of gravitation in flat space-time the 2-post-Newtonian approximation of a nonstationary spherically symmetric star is derived. The theory forces retarded effects for one part of the solutions of the 2-post-Newtonian approximation. The equations of motion and the conserved total energy of a nonstationary star are given up to 2-post-Newtonian order. The solution in the exterior of the body is studied to this accuracy. Birkhoff's theorem is violated. For the special case of a static spherically symmetric star we get deviations of the exterior solution in the 2-post-Newtonian approximation relative to Einstein's theory.