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This paper extends the Magnusian framework, a mathematical tool that generates phase-space evolution through nested Poisson brackets, to systems experiencing energy dissipation and time-delayed interactions. The authors apply this generalized framework to binary orbital systems where gravitational radiation causes energy loss, specifically deriving a Magnusian generator for Newtonian orbits with leading 2.5 post-Newtonian radiation-reaction effects. The resulting generator successfully describes cycle-to-cycle orbital evolution in agreement with numerical simulations.
Why it matters
This work provides a new computational method for modeling gravitational wave sources like binary black holes and neutron stars, which are key targets for gravitational wave observatories. The discrete evolution map approach could offer computational advantages over traditional methods for long-term orbital simulations needed to predict gravitational wave signals.
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⚠️ Preprint – Noch nicht peer-reviewed
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Abstract: The Magnusian is a phase-space function that generates finite-time evolution through nested Poisson brackets. It is related to several familiar generators of classical dynamics, including the radial action, the eikonal phase and related quantities. In this work, we extend the Magnusian framework to systems with dissipation and nonlocal-in-time interactions using the in-in formalism, also known as the Schwinger-Keldysh or Galley formalism. This framework is particularly natural for binary dynamics, where integrating out the mediating gravitational field can produce both dissipative radiation-reaction effects and hereditary, nonlocal-in-time interactions. We derive the generalized Magnusian and show that it continues to generate finite-time evolution. As an application, we construct the Magnusian for Newtonian bound motion subject to the leading 2.5PN radiation-reaction force. The resulting generator defines a discrete evolution map from one cycle to the next and describes the evolution of the system in agreement with numerical solutions.