Effective one-body formalism: Difference between revisions

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The effective one-body or EOB formalism, 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]. The theory allows calculations to not only be made in particular limits 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, it leads to results faster than numerical relativity. Rather than being considered distinct from these other approaches to the two-body problem, the EOB formalism is a way to resum information from other methods^[3]. It does so by mapping the general two-body problem to that of a test-particle in an effective metric. The method was used in the data-analysis of gravitational wave detectors such as LIGO and Virgo^[4].

References

^ Buonnano, A.; Damour, T. (1999), "Effective one-body approach to general relativistic two-body dynamics", Phys. Rev. D, 59 (8)
^ Damour, T.; Nagar, A. (2011), "The Effective One-Body Description of the Two-Body Problem", in Blanchet, L.; Spallicci, A.; Whiting, B. (eds.), Mass and Motion in General Relativity, Springer, pp. 211–252
^ Bini, D.; Damour, T.; Geralico, A. (2017), "High-Order Post-Newtonian Contributions to Gravitational Self-force Effects in Black Hole Spacetimes", in Gosse, L.; Natalini, R. (eds.), Innovative Algorithms and Analysis, Springer, pp. 25–77
^ Abbott, B. P.; et al. (LIGO Scientific Collaboration and Virgo Collaboration) (7 June 2016). "GW150914: First results from the search for binary black hole coalescence with Advanced LIGO". Physical Review Letters. 93 (12).

[1] Buonnano, A.; Damour, T. (1999), "Effective one-body approach to general relativistic two-body dynamics", Phys. Rev. D, 59 (8)

[2] Damour, T.; Nagar, A. (2011), "The Effective One-Body Description of the Two-Body Problem", in Blanchet, L.; Spallicci, A.; Whiting, B. (eds.), Mass and Motion in General Relativity, Springer, pp. 211–252

[3] Bini, D.; Damour, T.; Geralico, A. (2017), "High-Order Post-Newtonian Contributions to Gravitational Self-force Effects in Black Hole Spacetimes", in Gosse, L.; Natalini, R. (eds.), Innovative Algorithms and Analysis, Springer, pp. 25–77

[4] Abbott, B. P.; et al. (LIGO Scientific Collaboration and Virgo Collaboration) (7 June 2016). "GW150914: First results from the search for binary black hole coalescence with Advanced LIGO". Physical Review Letters. 93 (12).

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-}}</ref>. This gives it an advantage over methods that only work in particular stages or limits, such as [[post-Newtonian]] theory in the early inspiral, when the objects are at large separation, or [[linearized gravity|black hole perturbation theory]], when the two objects differ greatly in mass. In addition, it leads to results faster than [[numerical relativity]]. Rather than being considered distinct from these other approaches to the two-body problem, the EOB formalism is a way to [[Padé approximant|resum]] information from all these other methods<ref>{{Citation
+}}</ref>. The theory allows calculations to not only be made in particular limits limits, such as [[post-Newtonian]] theory in the early inspiral, when the objects are at large separation, or [[linearized gravity|black hole perturbation theory]], when the two objects differ greatly in mass. In addition, it leads to results faster than [[numerical relativity]]. Rather than being considered distinct from these other approaches to the two-body problem, the EOB formalism is a way to [[Padé approximant|resum]] information from other methods<ref>{{Citation
 |last=Bini
 |first=D.
@@ Line 43: / Line 43: @@
 |pages=25-77
 |publisher=Springer
-}}</ref>. It does so by mapping the general two-body problem to that of a test-particle in an effective [[Metric tensor (general relativity)|metric]]. This effective metric is not a solution to the [[Einstein equations]]. An important application of the effective one-body formalism is in the data-analysis of [[gravitational-wave observatory|gravitational wave detectors]] such as [[LIGO]] and [[Virgo interferometer|Virgo]]<ref>{{Cite journal |collaboration=LIGO Scientific Collaboration and Virgo Collaboration |last=Abbott |first=B. P. |date=7 June 2016 |title=GW150914: First results from the search for binary black hole coalescence with Advanced LIGO |journal=[[Physical Review Letters]] |volume=93 |issue=12}}</ref>.
+}}</ref>. It does so by mapping the general two-body problem to that of a test-particle in an effective [[Metric tensor (general relativity)|metric]]. The method was used in the data-analysis of [[gravitational-wave observatory|gravitational wave detectors]] such as [[LIGO]] and [[Virgo interferometer|Virgo]]<ref>{{Cite journal |collaboration=LIGO Scientific Collaboration and Virgo Collaboration |last=Abbott |first=B. P. |date=7 June 2016 |title=GW150914: First results from the search for binary black hole coalescence with Advanced LIGO |journal=[[Physical Review Letters]] |volume=93 |issue=12}}</ref>.
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