Coalescence of two spinning black holes: an effective one-body approach

By T. Damour. 2001

398 citations recorded by the source corpus.

We generalize to the case of spinning black holes a recently introduced ``effective one-body'' approach to the general relativistic dynamics of binary systems. The combination of the effective one-body approach, and of a Pad\'e definition of some crucial effective radial functions, is shown to define a dynamics with much improved post-Newtonian convergence properties, even for black hole separations of the order of $6 GM / c^2$. We discuss the approximate existence of a two-parameter family of ``spherical orbits'' (with constant radius), and, of a corresponding one-parameter family of ``last stable spherical orbits'' (LSSO). These orbits are of special interest for forthcoming LIGO/VIRGO/GEO gravitational wave observations. It is argued that for most (but not all) of the parameter space of two spinning holes the effective one-body approach gives a reliable analytical tool for describing the dynamics of the last orbits before coalescence. This tool predicts, in a quantitative way, how certain spin orientations increase the binding energy of the LSSO. This leads to a detection bias, in LIGO/VIRGO/GEO observations, favouring spinning black hole systems, and makes it urgent to complete the conservative effective one-body dynamics given here by adding (resummed) radiation reaction effects, and by constructing gravitational waveform templates that include spin effects. Finally, our approach predicts that the spin of the final hole formed by the coalescence of two arbitrarily spinning holes never approaches extremality.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/36de4200c77620faed59151933e5212661263e91

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In Astronomy and Astrophysics

1. T. Damour
2. D. Holz
3. Michela Mapelli
4. Maya Fishbach
5. Mario Spera
6. N. Giacobbo
7. E. Barausse
8. Ilya Mandel

Citations in the corpus

• Black Hole Mass and Spin Coevolution by Mergers (2002, background): “Post-Newtonian analyses (Blanchet 2002; Buonanno & Damour 1999; Damour 2001) show that finite mass ratio typically changes the LSO and its orbital constants by a factor of order η ≡ mM/(m+M)2 = q/(1 + q)2 ≤ 0.25.”
• Spinning black hole binary dynamics, scattering amplitudes, and effective field theory (2020, background): “As for the spinless case, these scattering observables are useful stepping stones for the construction of effective one-body Hamiltonians [2, 92, 93] which can be used to evaluate bound-state dynamics.”
• Observables and amplitudes for spinning particles and black holes (2019, positive): “Incorporating spin into a major theoretical platform for these experiments, the effective one-body formalism [16, 17], is well established in the PN approximation [18–24], and was recently extended to the PM approximation by means of a gauge-invariant spin holonomy [25].”
• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs (2018, background): “and effective aligned spin χeff appear in the phasing at higher orders [95, 115, 117].”
• Binary Black Hole Mergers in the First Advanced LIGO Observing Run (2016, neutral): “and the effective spin parameter [71–76]”