High-energy gravitational scattering and the general relativistic two-body problem
By T. Damour. 2017
272 citations recorded by the source corpus.
A technique for translating the classical scattering function of two gravitationally interacting bodies into a corresponding (effective one-body) Hamiltonian description has been recently introduced [Phys.\ Rev.\ D {\bf 94}, 104015 (2016)]. Using this technique, we derive, for the first time, to second-order in Newton's constant (i.e. one classical loop) the Hamiltonian of two point masses having an arbitrary (possibly relativistic) relative velocity. The resulting (second post-Minkowskian) Hamiltonian is found to have a tame high-energy structure which we relate both to gravitational self-force studies of large mass-ratio binary systems, and to the ultra high-energy quantum scattering results of Amati, Ciafaloni and Veneziano. We derive several consequences of our second post-Minkowskian Hamiltonian: (i) the need to use special phase-space gauges to get a tame high-energy limit; and (ii) predictions about a (rest-mass independent) linear Regge trajectory behavior of high-angular-momenta, high-energy circular orbits. Ways of testing these predictions by dedicated numerical simulations are indicated. We finally indicate a way to connect our classical results to the quantum gravitational scattering amplitude of two particles, and we urge amplitude experts to use their novel techniques to compute the 2-loop scattering amplitude of scalar masses, from which one could deduce the third post-Minkowskian effective one-body Hamiltonian.
Subfields: Astronomy and Astrophysics, Geophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/6d17321042c620f6a526e73a52d501575767818f
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Citations in the corpus
- Observables and amplitudes for spinning particles and black holes (2019, background): “classical and quantum corrections to gravitational potentials [38–51], and there has been significant recent progress in obtaining such corrections in the PM approximation [52–57].”
- Revisiting the second post-Minkowskian eikonal and the dynamics of binary black holes (2019, background): “ Γ2 D−3 2 Γ(D− 3) m 1 + m 2 b2D−7 ˆ (s− m 1 −m2 2) 2 − 4m 2 1m 2 (D− 2)2 − (D−3)((s−m2 1 − m 2) 2 − 4m2 1m 2 2) 4(D−2)2 ˙ . (2.33) The results in this subsection agree with results for D = 4 found in [11, 19, 13]. We have not considered the subleading triangle-like contribution explicitly in this su”
- Universality of ultra-relativistic gravitational scattering (2020, background): “The importance of such a result for computing the templates for actual gravitational-wave experiments have been stressed, in particular by Damour.”
- Scattering of spinning black holes from exponentiated soft factors (2018, background): “Interestingly, this matches their effective counterpart, as computed for instance in the worldline formalism, in the case where the operator Ocl is constant [32, 37].”
- On-shell heavy particle effective theories (2020, unknown): “[28–31].”
- Black hole binary dynamics from the double copy and effective theory (2019, methodology): “al Helicity To illustrate some essential features of our procedure for constructing amplitudes’ integrands in the post-Minkowskian expansion, we rst describe the 2PM order, discussed earlier in Refs. [20,22,48,58,60{63,108]. As discussed in Sec.2, the part of loop integrands that contributes to the ”
- Post-Minkowskian Hamiltonians in general relativity (2019, background): “This leads naturally to what has become known in the theory of General Relativity as the post-Minkowskian expansion [14–20].”
- Classical and quantum scattering in post-Minkowskian gravity (2019, methodology): “[19–23], and at the third post-Minkowskian (3PM) level (i.”
- Post-Minkowskian effective field theory for conservative binary dynamics (2020, background): “e PM expansion. At leading order the trajectory is represented by a straight line, and higher PM eects result in a series of corrections, which we parameterize in terms of the proper time as follows [65,93,94] v a(˝ 1) = u a+ X n (n)v a(˝ a); x a(˝ 1) = b a+ u a˝ a+ X n (n)x a(˝ a); (3.24) where ”
- Radiative contribution to classical gravitational scattering at the third order in G (2020, methodology): “[8, 10, 37] to transcribe, for any finite values of the masses and of γ, the 3PM-level radiationcorrected total scattering angle χ 3 into a corresponding value for the 3PM-level effective one-body potential (either in the Q Finsler-like form or the W potential one).”