Some remarks on the two-body-problem in geometrodynamics

The interest in the two body problem in geometrodynamics and its present status are discussed. Special consideration is given to time-symmetric initial data. An equation relating the “bare mass energy,” the potential energy and the “vibrational energy” at the initial moment is proposed. The significance of coordinate conditions in dynamical equations is discussed next. Conditions implying maximal slicings of spacetime and harmonic coordinates in those slices are considered in detail, as they seem to be well suited for numerical calculations and for interpretation of the results of such calculations.