The General Relativistic Two Body Problem and the Effective One Body Formalism

Abstract

A new analytical approach to the motion and radiation of (comparable mass) binary systems has been introduced in 1999 under the name of 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.

41 pages, 4 figures, contribution to the proceedings of the conference "Relativity and Gravitation - 100 years after Einstein in Prague", Prague, 25-29 June 2012

References in corpus (33)

• Inspiral, merger and ring-down of equal-mass black-hole binaries
• Total recoil: the maximum kick from nonspinning black-hole binary inspiral
• Inspiral, merger and ringdown of unequal mass black hole binaries: a multipolar analysis
• High-accuracy waveforms for binary black hole inspiral, merger, and ringdown
• Toward faithful templates for non-spinning binary black holes using the effective-one-body approach
• Faithful Effective-One-Body waveforms of small-mass-ratio coalescing black-hole binaries
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-spinning, equal-mass black holes
• An improved analytical description of inspiralling and coalescing black-hole binaries
• Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling
• Where post-Newtonian and numerical-relativity waveforms meet
• Comparing Effective-One-Body gravitational waveforms to accurate numerical data
• Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion
• A data-analysis driven comparison of analytic and numerical coalescing binary waveforms: nonspinning case
• Using Full Information When Computing Modes of Post-Newtonian Waveforms From Inspiralling Compact Binaries in Circular Orbit
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Accurate Effective-One-Body waveforms of inspiralling and coalescing black-hole binaries
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-precessing, spinning, equal-mass black holes
• Gravitational Recoil during Binary Black Hole Coalescence using the Effective One Body Approach
• Faithful Effective-One-Body waveforms of equal-mass coalescing black-hole binaries
• The third and a half post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries
• Gravitational radiation reaction along general orbits in the effective one-body formalism
• Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring
• Analytic modelling of tidal effects in the relativistic inspiral of binary neutron stars
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• Binary black hole merger in the extreme mass ratio limit
• Comparison between numerical-relativity and post-Newtonian waveforms from spinning binaries: the orbital hang-up case
• The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
• Extreme Mass-Ratio Inspirals in the Effective-One-Body Approach: Quasi-Circular, Equatorial Orbits around a Spinning Black Hole
• Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems
• Binary black hole coalescence in the extreme-mass-ratio limit: testing and improving the effective-one-body multipolar waveform
• Final spin of a coalescing black-hole binary: an Effective-One-Body approach
• Suitability of hybrid gravitational waveforms for unequal-mass binaries
• Constraints and the E10 Coset Model

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• Interpreting Binary Neutron Star Mergers: Describing the Binary Neutron Star Dynamics, Modelling Gravitational Waveforms, and Analyzing Detections
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• Dynamics of Quadruple Systems Composed of Two Binaries: Stars, White Dwarfs, and Implications for Ia Supernovae
• Gyroscopes orbiting black holes: A frequency-domain approach to precession and spin-curvature coupling for spinning bodies on generic Kerr orbits
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• Evolution of diffuse scalar clouds around binary black holes
• Post-Newtonian templates for gravitational waves from compact binary inspirals
• The two-body potential of Vainshtein screened theories
• Improving the convergence order of binary neutron star merger simulations in the Baumgarte-Shapiro-Shibata-Nakamura formulation
• Particle motion under the conservative piece of the self-force is Hamiltonian
• The H-graph with equal masses in terms of multiple polylogarithms
• The exterior spacetime of relativistic stars in scalar-Gauss-Bonnet gravity
• Fast Evolution and Waveform Generator for Extreme-Mass-Ratio Inspirals in Equatorial-Circular Orbits
• Role of dense matter in tidal deformations of inspiralling neutron stars and in gravitational waveform with unified equations of state
• Motion of a spinning particle under the conservative piece of the self-force is Hamiltonian to first order in mass and spin
• Symplectic mechanics of relativistic spinning compact bodies II.: Canonical formalism in the Schwarzschild spacetime
• A public framework for Feynman calculations and post-Newtonian gravity
• Comparing a Compact-Binary Mass-Shell Model with Select Observed Gravitational Waves