Post-adiabatic dynamics and waveform generation in self-force theory: an invariant pseudo-Hamiltonian framework
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918088806498304 |
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| author | Lewis, Jack Kakehi, Takafumi Pound, Adam Tanaka, Takahiro |
| author_facet | Lewis, Jack Kakehi, Takafumi Pound, Adam Tanaka, Takahiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08081 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Post-adiabatic dynamics and waveform generation in self-force theory: an invariant pseudo-Hamiltonian framework Lewis, Jack Kakehi, Takafumi Pound, Adam Tanaka, Takahiro General Relativity and Quantum Cosmology 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. |
| title | Post-adiabatic dynamics and waveform generation in self-force theory: an invariant pseudo-Hamiltonian framework |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2507.08081 |