Fourth post-Newtonian effective one-body dynamics

TL;DR

This paper transcribes the 4PN conservative two-body dynamics into the effective one-body formalism, introducing new potentials and higher-order terms, and compares the results with numerical self-force computations.

Contribution

It develops a novel strategy to incorporate nonlocal 4PN dynamics into the EOB framework using an infinite-order reduction to a local Hamiltonian.

Findings

Derived 4PN EOB potentials A(r) and D̄(r)

Included 5PN and 5.5PN higher-order conservative terms

Compared analytical results with numerical self-force data

Abstract

The conservative dynamics of gravitationally interacting two-point-mass systems has been recently determined at the fourth post-Newtonian (4PN) approximation [T.Damour, P.Jaranowski, and G.Sch\"afer, Phys. Rev. D 89, 064058 (2014)], and found to be nonlocal in time. We show how to transcribe this dynamics within the effective one-body (EOB) formalism. To achieve this EOB transcription, we develop a new strategy involving the (infinite-)order-reduction of a nonlocal dynamics to an ordinary action-angle Hamiltonian. Our final, equivalent EOB dynamics comprises two (local) radial potentials, $A(r)$ and $\bar{D}(r)$, and a nongeodesic mass-shell contribution $Q(r,p_r)$ given by an infinite series of even powers of the radial momentum $p_r$. Using an effective action technique, we complete our 4PN-level results by deriving two different, higher-order conservative contributions linked to tail-transported hereditary effects: the 5PN-level EOB logarithmic terms, as well as the 5.5PN-level, half-integral terms. We compare our improved analytical knowledge to previous, numerical gravitational-self-force computation of precession effects.