Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism

TL;DR

This paper investigates how conservative Gravitational Self-Force data in a Schwarzschild background can inform and constrain the conservative sector of the Effective One Body formalism. By relating the GSF-determined LSO frequency shift to the ν-linear corrections of the EOB A(u;ν) potential and comparing with NR-EOB fits, it demonstrates that GSF data help break degeneracies in the parameters a5 and a6 and suggests additional GSF-derived observables (eccentric orbits and zero-binding zoom-whirl) to further illuminate the EOB building blocks. It also analyzes the role of logarithmic terms that first appear at 4PN and examines how Detweiler’s redshift and PN expansions reflect running coefficients in the EOB potentials. The study outlines concrete avenues—including small-eccentricity diagnostics and the zero-binding zoom-whirl orbit—to extract precise information on the strong-field behavior of the EOB potentials, thereby strengthening the link between GSF, NR, and EOB modeling for gravitational-wave astronomy.

Abstract

We discuss various ways in which the computation of conservative Gravitational Self Force (GSF) effects on a point mass moving in a Schwarzschild background can inform us about the basic building blocks of the Effective One-Body (EOB) Hamiltonian. We display the information which can be extracted from the recently published GSF calculation of the first-GSF-order shift of the orbital frequency of the last stable circular orbit, and we combine this information with the one recently obtained by comparing the EOB formalism to high-accuracy numerical relativity (NR) data on coalescing binary black holes. The information coming from GSF data helps to break the degeneracy (among some EOB parameters) which was left after using comparable-mass NR data to constrain the EOB formalism. We suggest various ways of obtaining more information from GSF computations: either by studying eccentric orbits, or by focussing on a special zero-binding zoom-whirl orbit. We show that logarithmic terms start entering the post-Newtonian expansions of various (EOB and GSF) functions at the fourth post-Newtonian (4PN) level, and we analytically compute the first logarithm entering a certain, gauge-invariant "redshift" GSF function (defined along the sequence of circular orbits).