Third post-Newtonian higher order ADM Hamilton dynamics for two-body point-mass systems

The paper presents the conservative dynamics of two-body point-mass systems up to the third post-Newtonian order ${(1/c}^{6}).$ The two-body dynamics is given in terms of a higher order ADM Hamilton function which results from a third post-Newtonian Routh functional for the total field-plus-matter system. The applied regularization procedures, together with making use of distributional differentiation of homogeneous functions, give unique results for the terms in the Hamilton function apart from the coefficient of the term $(\ensuremath{\nu}{p}_{i}{\ensuremath{\partial}}_{i}{)}^{2}{r}^{\ensuremath{-}1}.$ The result suggests an invalidation of the binary point-mass model at the third post-Newtonian order and indicates the emergence of black holes as a model for the mass points.