Scattering of spinning black holes from exponentiated soft factors

By A. Guevara, Alexander Ochirov, J. Vines. Journal of High Energy Physics, 2018

265 citations recorded by the source corpus.

We provide evidence that the classical scattering of two spinning black holes is controlled by the soft expansion of exchanged gravitons. We show how an exponentiation of Cachazo-Strominger soft factors, acting on massive higher-spin amplitudes, can be used to find spin contributions to the aligned-spin scattering angle, conjecturally extending previously known results to higher orders in spin at one-loop order. The extraction of the classical limit is accomplished via the on-shell leading-singularity method and using massive spinor-helicity variables. The three-point amplitude for arbitrary-spin massive particles minimally coupled to gravity is expressed in an exponential form, and in the infinite-spin limit it matches the effective stress-energy tensor of the linearized Kerr solution. A four-point gravitational Compton amplitude is obtained from an extrapolated soft theorem, equivalent to gluing two exponential three-point amplitudes, and becomes itself an exponential operator. The construction uses these amplitudes to: 1) recover the known tree-level scattering angle at all orders in spin, 2) recover the known one-loop linear-in-spin interaction, 3) match a previous conjectural expression for the one-loop scattering angle at quadratic order in spin, 4) propose new one-loop results through quartic order in spin. These connections link the computation of higher-multipole interactions to the study of deeper orders in the soft expansion.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/fe5569b9997667be6feaaeea5a0a6c22c19a0322

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. T. Damour
2. Rafael A. Porto
3. G. Kalin
4. Alexander Ochirov
5. D. O’Connell
6. A. Luna
7. R. Roiban
8. Z. Bern

In Nuclear and High Energy Physics

1. T. Damour
2. Alexander Ochirov
3. Rafael A. Porto
4. H. Johansson
5. G. Kalin
6. D. O’Connell
7. A. Luna
8. R. Roiban

Citations in the corpus

• Double copy for massive quantum particles with spin (2019, methodology): “rmulae. The gauge-theoretic amplitudes A(1fag i ;2 fbg | ;3 + c) = ( 1) bscigTc i| h1a2bi2s m2s 1 x3; (3.22a) A(1fag i ;2 fbg | ;3 c) = ( 1) bsc+1igTc i| [1a2b]2s m2s 1 x 1 3 ; (3.22b) 4In ref. [8] the same amplitudes were derived from the Noether energy-momentum tensor in ate space symmetrized with”
• From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist) (2019, background): “For example, let us consider the 1PM amplitude including only one of the particles carrying spin a, which reads (recall μM = m1m2) [23] M1PM(q,p,a) = 8π Gμ2M2 q2 γ ∑”
• From boundary data to bound states (2019, background): “The inclusion of spin, both in the EFT approach [71–78] and in scattering amplitudes [40, 44, 48, 53, 79–82], introduces rich new structures.”
• Post-Minkowskian effective field theory for conservative binary dynamics (2020, unknown): “[3, 62–91].”
• Post-Minkowskian Hamiltonians in general relativity (2019, background): “[20] A.”
• Classical and quantum scattering in post-Minkowskian gravity (2019, background): “] Let us also mention some further (partly conjectural) work concerning the link between the gravitational scattering amplitude of spinning particles and the classical gravitational interaction of Kerr black holes [29–33], as well as work on the computation of classically measurable quantities from ”
• Radiative contribution to classical gravitational scattering at the third order in G (2020, unknown): “[26–34] for PM-type works on spinning bodies.”
• Revisiting the second post-Minkowskian eikonal and the dynamics of binary black holes (2019, background): “See [21, 22, 23] for a recent analysis of the amplitude approach to this case.”
• Spinning black hole binary dynamics, scattering amplitudes, and effective field theory (2020, methodology): “In the presence of spins, however, the known results from EFT or scattering angles are either limited to leading order in G or to special configurations of spins [23, 38, 59, 61, 63].”
• On-shell heavy particle effective theories (2020, methodology): “On the PM side, it has also recently been shown that quantum scattering amplitudes can be used to extract fully relativistic information about the classical scattering process [18–27].”
• Observables and amplitudes for spinning particles and black holes (2019, methodology): “in quantum numbers ncontinues to reproduce the same expressions at lower orders in the spin operators. We have seen this explicitly here for the linear-in-spin level, up to spin 1, and the results of [9, 10, 12] strongly suggest that an application of our formalism – 20 – to minimally coupled amplit”
• Scattering amplitudes for all masses and spins (2017, background): “−−−−−−→ 〈η31〉〈η32〉 〈21〉 = [3|p2|1〉[3|p1|2〉 m2〈21〉 = [32][31] [21] (2.”
• Kerr black holes as elementary particles (2019, unknown): “Following the work of Guevara [14], it was shown in [15] and [16] that the potential for Kerr black holes was indeed reproduced relativistically to all orders in the multipole expansion from minimal coupling.”