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arXiv · 2510.26874

Gravitational waveforms from restriction theory and rapid-decay homology

Giacomo Brunello·Vsevolod Chestnov·Giulio Crisanti·Mathieu Giroux·Sid Smith
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Abstract

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.

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Giacomo Brunello, Vsevolod Chestnov, Giulio Crisanti, Mathieu Giroux, Sid Smith. 2025-10-30. Gravitational waveforms from restriction theory and rapid-decay homology. https://arxiv.org/abs/2510.26874

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