The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach

Abstract

Within an effective field theory method to general relativity, we calculate the fifth-order post--Newtonian (5 PN) Hamiltonian dynamics also for the tail terms, extending earlier work on the potential contributions, working in harmonic coordinates. Here we calculate independently all (local) 5 PN contributions to the tail terms using the in--in formalism, on which we give a detailed account. The five expansion terms of the Hamiltonian in the effective one body (EOB) approach, $q_{82},q_{63},q_{44},\overline{d_5}$ and $a_6$, can all be determined from the local contributions to periastron advance $K^{\mathrm{loc},\mathrm{h}}(\hat{E},j)$, without further assumptions on the structure of the symmetric mass ratio, $\hat{I}½$, of the expansion coefficients of the scattering angle $\ddot{I}{‡}_k$. The $O(\hat{I}{½}^2)$ contributions to the 5 PN EOB parameters have been unknown in part before. We perform comparisons of our analytic results with the literature and also present numerical results on some observables.

42 pages LATEX, several figures, published version