Effective one-body formalism

The effective one-body approach compared to other methods

The effective one-body or EOB approach is an analytical approach to the gravitational two-body problem in general relativity. It was introduced by Alessandra Buonanno and Thibault Damour in 1999.^[1] It aims to describe all different phases of the two-body dynamics in a single analytical method.^[2]

Classical gravity theory allows analytical calculations to be made in particular limits, such as post-Newtonian theory in the early inspiral, when the objects are at large separation, or black hole perturbation theory, when the two objects differ greatly in mass. In addition, they lead to results faster than numerical relativity.

Rather than being considered distinct from these independent approaches to the two-body problem, the EOB approach is a way to resum information from other independent methods.^[3] It does so by mapping the general two-body problem to that of a test particle in an effective metric. The EOB approach was used in the data analysis of gravitational wave detectors such as LIGO and Virgo.^[4]

References

^ Buonanno, A.; Damour, T. (1999-03-08). "Effective one-body approach to general relativistic two-body dynamics". Physical Review D. 59 (8). American Physical Society (APS): 084006. arXiv:gr-qc/9811091. Bibcode:1999PhRvD..59h4006B. doi:10.1103/physrevd.59.084006. ISSN 0556-2821. S2CID 14951569.
^ Damour, Thibault; Nagar, Alessandro (2009). "The Effective One-Body Description of the Two-Body Problem". Mass and Motion in General Relativity. Dordrecht: Springer Netherlands. pp. 211–252. arXiv:0906.1769. doi:10.1007/978-90-481-3015-3_7. ISBN 978-90-481-3014-6. S2CID 15391998.
^ Bini, Donato; Damour, Thibault; Geralico, Andrea (2017). "High-Order Post-Newtonian Contributions to Gravitational Self-force Effects in Black Hole Spacetimes". Innovative Algorithms and Analysis. Springer INdAM Series. Vol. 16. Cham: Springer International Publishing. pp. 25–77. doi:10.1007/978-3-319-49262-9_2. ISBN 978-3-319-49261-2. ISSN 2281-518X.
^ Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; et al. (LIGO Scientific Collaboration and Virgo Collaboration) (2016-06-07). "GW150914: First results from the search for binary black hole coalescence with Advanced LIGO". Physical Review D. 93 (12): 122003. arXiv:1602.03839. Bibcode:2016PhRvD..93l2003A. doi:10.1103/physrevd.93.122003. ISSN 2470-0010. PMC 7430253. PMID 32818163. S2CID 217628912.

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[1] Buonanno, A.; Damour, T. (1999-03-08). "Effective one-body approach to general relativistic two-body dynamics". Physical Review D. 59 (8). American Physical Society (APS): 084006. arXiv:gr-qc/9811091. Bibcode:1999PhRvD..59h4006B. doi:10.1103/physrevd.59.084006. ISSN 0556-2821. S2CID 14951569.

[2] Damour, Thibault; Nagar, Alessandro (2009). "The Effective One-Body Description of the Two-Body Problem". Mass and Motion in General Relativity. Dordrecht: Springer Netherlands. pp. 211–252. arXiv:0906.1769. doi:10.1007/978-90-481-3015-3_7. ISBN 978-90-481-3014-6. S2CID 15391998.

[3] Bini, Donato; Damour, Thibault; Geralico, Andrea (2017). "High-Order Post-Newtonian Contributions to Gravitational Self-force Effects in Black Hole Spacetimes". Innovative Algorithms and Analysis. Springer INdAM Series. Vol. 16. Cham: Springer International Publishing. pp. 25–77. doi:10.1007/978-3-319-49262-9_2. ISBN 978-3-319-49261-2. ISSN 2281-518X.

[4] Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; et al. (LIGO Scientific Collaboration and Virgo Collaboration) (2016-06-07). "GW150914: First results from the search for binary black hole coalescence with Advanced LIGO". Physical Review D. 93 (12): 122003. arXiv:1602.03839. Bibcode:2016PhRvD..93l2003A. doi:10.1103/physrevd.93.122003. ISSN 2470-0010. PMC 7430253. PMID 32818163. S2CID 217628912.

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