Constants of Motion and Fundamental Frequencies at Fourth Post-Newtonian Order

par David Trestini (University of Southampton)

mercredi 18 févr. 2026, 14:45 → 16:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Séminaire Amplitudes et Gravitation sur l'Yvette (IHES/IPhT)

In the first part of my talk, I will discuss the distinction between (i) the conservativeenergy, which is conserved under the conservative equations of motion, and (ii) the binding energy, which enters the flux-balance laws. The difference between these two energies is called a Schott term and was historically expected to vanish for circular orbits. But I will show that at 4PN, the Schott term does not vanish due to a hereditary piece in the dissipative equations of motion. I will explain how the Schott term can link the notions of orbital and waveform frequencies and properly ensure the absence of arbitrary constants in physical observables within the post-Newtonian formalism.

In the second part of my talk, I will present the derivation of the action-angle 4PN conservative Hamiltonian for bound eccentric systems, including the 4PN tail term. The latter appears as an enhancement function of the eccentricity, which takes the form of a well-controlled infinite sum, which is resummed in a simple form such as to maintain a 10^-5 relative accuracy for any eccentricity. It is then immediate to deduce the 4PN links between the conservative constants of motion (energy and angular momentum) and the fundamental (radial and azimuthal) orbital frequencies. From there, I obtain the 4PN redshift, which is in perfect agreement with analytical self-force.

 

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