The general relativistic two body problem

TL;DR

This paper reviews the Effective One Body (EOB) formalism for modeling the two-body problem in General Relativity, highlighting its accuracy and potential for gravitational wave data analysis through comparisons with numerical simulations.

Contribution

It introduces and discusses recent developments of the EOB formalism, demonstrating its effectiveness in modeling binary systems and gravitational waveforms.

Findings

EOB formalism accurately models binary black hole and neutron star dynamics.

Comparisons show EOB predictions match Numerical Relativity simulations.

EOB combined with other methods aids in gravitational wave data analysis.

Abstract

The two-body problem in General Relativity has been the subject of many analytical investigations. After reviewing some of the methods used to tackle this problem (and, more generally, the N-body problem), we focus on a new, recently introduced approach to the motion and radiation of (comparable mass) binary systems: the Effective One Body (EOB) formalism. We review the basic elements of this formalism, and discuss some of its recent developments. Several recent comparisons between EOB predictions and Numerical Relativity (NR) simulations have shown the aptitude of the EOB formalism to provide accurate descriptions of the dynamics and radiation of various binary systems (comprising black holes or neutron stars) in regimes that are inaccessible to other analytical approaches (such as the last orbits and the merger of comparable mass black holes). In synergy with NR simulations, post-Newtonian (PN) theory and Gravitational Self-Force (GSF) computations, the EOB formalism is likely to provide an efficient way of computing the very many accurate template waveforms that are needed for Gravitational Wave (GW) data analysis purposes.