Gravitational two-body scattering event with gravitational waves.
State-of-the-art predictions can now be used to create waveform models for next-generation gravitational-wave detectors.
An international team, including researchers at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) in the Potsdam Science Park, has calculated with record precision how two black holes deflect each other's paths when they fly past one another under the influence of their mutual gravitational attraction. This novel result covers any mass ratio.
Gravitational-wave observatories routinely detect ripples in spacetime from colliding black holes. Decoding these signals requires predictions of black-hole motion, and these predictions must be accurate enough to keep pace with ever more sensitive detectors. Recently, methods borrowed from particle physics — treating gravity with the tools of quantum field theory developed for colliders — have driven rapid progress.
Using their worldline quantum field theory approach and high-performance computers, the researchers computed the energy-conserving part of the deflection angle at the fifth order of approximation in the strength of gravity. The key advance is completing the mass dependence at this order, where earlier results applied only to highly unequal pairs. The explicit analytic answer involves exotic mathematical functions related to higher-dimensional generalizations of torii, and a subtle infinity at one special fly-by speed cancels in their refined definition of energy-conserving effects. This state-of-the-art prediction may now be used for the waveform models required for next-generation gravitational wave detectors.
An international team, including researchers at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) in the Potsdam Science Park, has calculated with record precision how two black holes deflect each other's paths when they fly past one another under the influence of their mutual gravitational attraction. This novel result covers any mass ratio.
Gravitational-wave observatories routinely detect ripples in spacetime from colliding black holes. Decoding these signals requires predictions of black-hole motion, and these predictions must be accurate enough to keep pace with ever more sensitive detectors. Recently, methods borrowed from particle physics — treating gravity with the tools of quantum field theory developed for colliders — have driven rapid progress.
Using their worldline quantum field theory approach and high-performance computers, the researchers computed the energy-conserving part of the deflection angle at the fifth order of approximation in the strength of gravity. The key advance is completing the mass dependence at this order, where earlier results applied only to highly unequal pairs. The explicit analytic answer involves exotic mathematical functions related to higher-dimensional generalizations of torii, and a subtle infinity at one special fly-by speed cancels in their refined definition of energy-conserving effects. This state-of-the-art prediction may now be used for the waveform models required for next-generation gravitational wave detectors.
Paper abstract
Using the worldline quantum field theory formalism, we compute conservative contributions to the scattering angle and impulse for classical black hole scattering at fifth post-Minkowskian (5PM) and second self-force (2SF) order. This four-loop calculation involves non-planar Feynman integrals and requires advanced integration-by-parts reduction, novel differential-equation strategies, and efficient boundary-integral algorithms to solve a system of hundreds of master integrals in four integral families on high-performance computing systems. The resulting function space includes multiple polylogarithms as well as iterated integrals with a K3 period, which generate a spurious velocity divergence at v/c = √8/3, γ = 3. This divergence is present in the potential region and must be canceled by contributions from the radiative memory region, while its dimensional-regularisation pole should cancel against the radiative tail region. As the standard use of Feynman propagators fails to ensure this cancellation, we instead propose a “(γ-3)” conservative prescription that realises both cancellations, leading to a physically sensible answer. All available low-velocity checks of our result against the post-Newtonian literature are satisfied.
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Media contact:
Dr. Elke Müller
Press Officer AEI Potsdam, Scientific Coordinator
Tel: +49 331 567-7303
Email: elke.mueller@aei.mpg.de
Publication Driesse, M.; Jakobsen, G. U.; Mogull, G.; Nega, C.; Plefka, J.; Sauer, B.; Usovitsch, J.
Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self-Force Order. Physical Review Letters 137, 081402 (2026)
MPG.PuRe - DOI - pre-print
