Gravitational waveforms from restriction theory and rapid-decay homology

Fuente: arXiv
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Autores principales: Brunello, Giacomo, Chestnov, Vsevolod, Crisanti, Giulio, Giroux, Mathieu, Smith, Sid
Formato: Preprint
Publicado: 2025
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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