Gravitational waveforms from restriction theory and rapid-decay homology
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911241220390912 |
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| author | Brunello, Giacomo Chestnov, Vsevolod Crisanti, Giulio Giroux, Mathieu Smith, Sid |
| author_facet | Brunello, Giacomo Chestnov, Vsevolod Crisanti, Giulio Giroux, Mathieu Smith, Sid |
| contents | We present a systematic framework for computing frequency-domain gravitational waveforms from relativistic binary scattering in different asymptotic regimes. The method yields a controlled series expansion that can in principle be extended to arbitrary order in the relevant kinematic parameter. By combining differential-equation techniques with restriction theory and algebraic-geometry methods for impact-parameter-space Fourier integrals, we derive recursion relations that generate the leading-order (tree-level) waveform in both the soft-emission and post-Newtonian regimes, establishing a proof of principle for extending the approach to higher-loop computations. Finally, following constraints from rapid-decay homology, we show that the Fourier integrals underlying the waveform satisfy epsilon-form differential equations mixing Bessel- and exponential-type kernels, marking a first step toward uncovering the analytic structure of the exact solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26874 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gravitational waveforms from restriction theory and rapid-decay homology Brunello, Giacomo Chestnov, Vsevolod Crisanti, Giulio Giroux, Mathieu Smith, Sid High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics We present a systematic framework for computing frequency-domain gravitational waveforms from relativistic binary scattering in different asymptotic regimes. The method yields a controlled series expansion that can in principle be extended to arbitrary order in the relevant kinematic parameter. By combining differential-equation techniques with restriction theory and algebraic-geometry methods for impact-parameter-space Fourier integrals, we derive recursion relations that generate the leading-order (tree-level) waveform in both the soft-emission and post-Newtonian regimes, establishing a proof of principle for extending the approach to higher-loop computations. Finally, following constraints from rapid-decay homology, we show that the Fourier integrals underlying the waveform satisfy epsilon-form differential equations mixing Bessel- and exponential-type kernels, marking a first step toward uncovering the analytic structure of the exact solution. |
| title | Gravitational waveforms from restriction theory and rapid-decay homology |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2510.26874 |