Post-adiabatic dynamics and waveform generation in self-force theory: an invariant pseudo-Hamiltonian framework

2025/07/10 by Lewis, Jack, Kakehi, Takafumi, Pound, Adam +1 · 6 citations
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2507.08081

Abstract

Gravitational waveform modeling in self-force theory has reached a mature stage in recent years, with fast and accurate models emerging at both adiabatic (0PA) and first post-adiabatic (1PA) orders in a multiscale expansion. Here, we provide a gauge-invariant 1PA waveform-generation framework that involves no direct calculation of the (gauge-dependent) self-force. To achieve this, we recast the multiscale framework in a pseudo-Hamiltonian form, working on the six-dimensional phase space intrinsic to the multiscale expansion. We characterize the gauge freedom on phase space and show how a localization procedure avoids nonlocal-in time effects in the 1PA dynamics. We find a conservative Hamiltonian structure can be naturally embedded into the complete, dissipative 1PA pseudo-Hamiltonian dynamics, giving rise to natural definitions of the conserved energy, angular momentum, and radial and polar actions. As a byproduct, we clarify that the on-shell value of the conservative Hamiltonian is equal to the mechanical energy historically predicted by the first law of binary black hole mechanics.

Citations

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Cited by

• Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary
• Hybrid waveform model for asymmetric spinning binaries: Self-force meets post-Newtonian theory
• Transition-to-plunge self-force waveforms with a spinning primary
• Systematic errors in fast relativistic waveforms for Extreme Mass Ratio Inspirals
• Estimating High-Order Time Derivatives of Kerr Orbital Functionals
• Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime

Related

• Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary
• Post-adiabatic waveform-generation framework for asymmetric precessing binaries
• High-order comparisons between post-Newtonian and perturbative self forces
• Local-in-Time Conservative Binary Dynamics at Fifth Post-Minkowskian and First Self-Force Orders
• Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime