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

TL;DR

This paper explores how gravitational self-force calculations can enhance the Effective One-Body formalism for modeling binary black hole systems, combining analytical and numerical data to improve accuracy in gravitational wave predictions.

Contribution

It demonstrates how GSF data can refine EOB models by breaking parameter degeneracies and suggests new methods to extract further information from GSF computations.

Findings

GSF data helps constrain EOB parameters more precisely.

Logarithmic terms appear at 4PN order in post-Newtonian expansions.

Analytical computation of the first logarithm in a gauge-invariant GSF function.

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).