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Relativity in Modern Physics$
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Nathalie Deruelle and Jean-Philippe Uzan

Print publication date: 2018

Print ISBN-13: 9780198786399

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198786399.001.0001

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The two-body problem: an effective-one-body approach

The two-body problem: an effective-one-body approach

Written in collaboration with Félix-Louis Julié

(p.574) 16 The two-body problem: an effective-one-body approach
Relativity in Modern Physics

Nathalie Deruelle

Jean-Philippe Uzan

Oxford University Press

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

Keywords:   effective-one-body approach, two-body problem, general relativity, equations of motion, waveform, Kerr black hole, waveform templates

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