Novel Approach to Binary Dynamics: Application to the Fifth Post-Newtonian Level

We introduce a new methodology for deriving the conservative dynamics of gravitationally interacting binary systems. Our approach combines, in a novel way, several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, gravitational self-force, and effective one body. We apply our method to the derivation of the fifth post-Newtonian dynamics. By restricting our results to the third post-Minkowskian level, we give the first independent confirmation of the recent result of Bern et al. [Phys. Rev. Lett. 122, 201603 (2019)]. We also offer checks for future fourth post-Minkowskian calculations. Our technique can, in principle, be extended to higher orders of perturbation theory.

Figure 1

Schematic representation of the theoretical tools used to obtain the various contributions to the 5PN-accurate local Hamiltonian. These contributions are keyed on the horizontal axis by powers of $u=GM/r$ and squared momentum $p^2\sim p_r^2\sim p_t^2$ and on the vertical axis by powers of $\nu \equiv m_1{m}_2/(m_1+m_2{)}^2$. The bullets indicate the coefficients determined for the first time in the present Letter. The question marks denote the only two missing coefficients.