Gravitational waveforms: A tale of two formalisms

Journal Article · 21 June 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.109.125008 · OSTI ID:2376237

Bini, Donato ; Damour, Thibault; De Angelis, Stefano ; Geralico, Andrea ; Herderschee, Aidan; Roiban, Radu; Teng, Fei

We revisit the quantum-amplitude-based derivation of the gravitational waveform emitted by the scattering of two spinless massive bodies at the third order in Newton’s constant, $h\sim G+G^2+G^3$ (one-loop level), and correspondingly update its comparison with its classically derived multipolar-post-Minkowskian counterpart. A spurious-pole-free reorganization of the one-loop five-point amplitude substantially simplifies the post-Newtonian expansion. We find complete agreement between the two results up to the fifth order in the small velocity expansion after taking into account three subtle aspects of the amplitude derivation: (1) in agreement with [A. Georgoudis , ], the term quadratic in the amplitude in the observable-based formalism [D. A. Kosower , ] generates a frame rotation by half the classical scattering angle; (2) the dimensional regularization of the infrared divergences of the amplitude introduces an additional $(d-4)/(d-4)$ finite term; and (3) zero-frequency gravitons are found to contribute additional terms both at order $h\sim G^1$ and at order $h\sim G^3$ when including disconnected diagrams in the observable-based formalism. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE
• OSTI ID: 2376237
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 12 Vol. 109; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English