3RD POST-NEWTONIAN HIGHER-ORDER ADM HAMILTON DYNAMICS FOR 2-BODY POINT-MASS SYSTEMS

The paper presents the conservative dynamics of two-body point-mass sy stems up to the third post-Newtonian order (1/c(6)). The two-body dyna mics is given in terms of a higher order ADM Hamilton function which r esults from a third post-Newtonian Routh functional for the total fiel d-plus-matter system. The applied regularization procedures, together with making use of distributional differentiation of homogeneous funct ions, give unique results for the terms in the Hamilton function apart from the coefficient of the term (nu p(i) delta(i))(2)r(-1). The resu lt suggests an invalidation of the binary point-mass model at the thir d post-Newtonian order and indicates the emergence of black holes as a model for the mass points.