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| EOBNR (effective-one-body) | |
|---|---|
| Name | EOBNR (effective-one-body) |
| Field | Gravitational physics |
| Introduced | 1999 |
| Creators | Alessandra Buonanno; Thibault Damour |
| Notable works | EOBNRv2; SEOBNRv4 |
EOBNR (effective-one-body)
EOBNR (effective-one-body) is a semi-analytical framework for modeling compact binary dynamics and gravitational-wave emission, developed to bridge post-Newtonian approximation and full numerical relativity. The approach, pioneered by Alessandra Buonanno and Thibault Damour, has been implemented and extended by collaborations including the LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Observatory to produce waveform families used in detections and parameter estimation. EOBNR integrates inputs from Isaac Newton-era two-body reductions, modern perturbation theory as formalized by Subrahmanyan Chandrasekhar, and computational results from groups at institutions such as Caltech, MIT, and the Max Planck Institute for Gravitational Physics.
EOBNR reformulates the relativistic two-body problem into an effective one-body problem, enabling mapping between a binary system and a particle moving in an effective spacetime; this mapping was developed in the context of research by Alessandra Buonanno and Thibault Damour and influenced subsequent work at Cornell University and the University of Cambridge. Early EOBNR models incorporated results from the post-Newtonian expansion community and were validated against simulations produced by groups at Caltech, NASA Jet Propulsion Laboratory, and the Max Planck Society. EOBNR underpins waveform families used by the LIGO Scientific Collaboration, the Virgo Collaboration, and the LISA Consortium for searches in data from detectors such as LIGO Hanford Observatory, LIGO Livingston Observatory, and Virgo Interferometer.
The theoretical basis of EOBNR rests on mappings introduced by Thibault Damour that convert the two-body Hamiltonian of general relativity into an effective Hamiltonian for a single particle in a deformed Schwarzschild or Kerr geometry, drawing on methods used by Paul Dirac and techniques from Regge calculus and black hole perturbation theory. It incorporates conservative dynamics from the post-Newtonian approximation community and radiation-reaction effects informed by results from Teukolsky equation studies and perturbative calculations by researchers at California Institute of Technology and Queen Mary University of London. The formulation uses resummation techniques inspired by work associated with Andrei Sakharov-era scattering theory and analytic continuation methods applied in contexts like the S-matrix program at Princeton University.
EOBNR waveform families are constructed by combining the effective dynamics with multipolar gravitational-wave generation formalisms developed by experts affiliated with Yakov Zel'dovich-related perturbation theory and waveform decomposition methods used at Stanford University and Louisiana State University. Calibration employs numerical-relativity waveforms from teams including the Simulating eXtreme Spacetimes (SXS) Collaboration, the Georgia Tech Gravitational Wave Group, and the RIT (Rochester Institute of Technology) group to tune adjustable parameters in models like SEOBNRv4 and EOBNRv2. Template banks used by the LIGO Scientific Collaboration and Virgo Collaboration integrate EOBNR-derived waveforms alongside phenomenological models produced by groups at Cardiff University and Monash University for matched-filter searches in data from observatories including GEO600.
Comparisons between EOBNR predictions and numerical-relativity simulations have been performed against catalogs produced by the SXS Collaboration, the RIT group, and the BAM code teams at University of Jena and Max Planck Institute for Gravitational Physics, revealing close agreement in phasing and amplitude across mass ratios and spin configurations evaluated by researchers at Princeton University and University of Maryland. Discrepancies in late inspiral and plunge phases motivated iterative calibration campaigns involving groups at Caltech, Cornell University, and University of Illinois Urbana-Champaign, while longer-term efforts coordinated with the Einstein Toolkit community improved waveform length and accuracy for parameter estimation in analyses performed by the LIGO Scientific Collaboration.
EOBNR waveforms are integral to parameter estimation pipelines used by the LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration for interpreting events such as GW150914 and subsequent binary black hole detections announced by teams including researchers from Caltech, MIT, and the Max Planck Institute for Gravitational Physics. They are also employed in population synthesis studies conducted by groups at University of Cambridge and Monash University and in testing general relativity in the strong-field regime by collaborations involving the International Astronomical Union-affiliated working groups. Ongoing integration with space-based mission planning by the European Space Agency and the LISA Consortium extends EOBNR use to extreme-mass-ratio inspirals modeled by specialists at University College London and Leiden University.
Limitations of EOBNR include uncertainties for high mass-ratio systems, strong precession, and eccentric inspirals, prompting active development by teams at Caltech, MIT, University of Birmingham, and the Max Planck Institute for Gravitational Physics. Extensions to include higher-order multipoles, tidal effects relevant for neutron-star binaries studied by researchers at University of Illinois Urbana-Champaign and Rutgers University, and calibration against longer numerical-relativity runs from the SXS Collaboration are ongoing. Community efforts coordinated via the LIGO Scientific Collaboration and workshops at Perimeter Institute continue to refine EOBNR implementations and validate them for next-generation observatories like the Einstein Telescope and Cosmic Explorer.
The EOBNR formalism employs an effective Hamiltonian H_eff mapped from the real two-body Hamiltonian H_real via a mass-dependent energy map developed by Thibault Damour and collaborators, with canonical variables analogous to those used in Hamiltonian treatments by Ludwig Boltzmann and constraint structures examined by researchers at Imperial College London. Radiation-reaction forces are encoded through flux functions and waveform multipoles calibrated against numerical relativity from the SXS Collaboration, leading to phasing equations solved in time-domain integration schemes implemented by groups at Caltech and University of Cambridge. Key operational relations include the energy map, the effective metric potentials A(r) and B(r) with Padé resummation introduced in work associated with Vladimir Arnold-inspired dynamical systems, and waveform stitching procedures that join inspiral, plunge, merger, and ringdown using quasi-normal-mode spectra computed following methods by S. Chandrasekhar and teams at the Max Planck Institute for Gravitational Physics.