Journal article
Gravitational waveforms from restriction theory and rapid-decay homology
- 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 ε-form differential equations mixing Bessel- and exponential-type kernels, marking a first step toward uncovering the analytic structure of the exact solution.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
-
-
(Preview, Accepted manuscript, pdf, 699.4KB, Terms of use)
-
- Publisher copy:
- 10.1103/ynk9-ykw7
Authors
+ UK Research and Innovation
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- Funder identifier:
- https://ror.org/001aqnf71
- Grant:
- UKRI FLF MR/Y003829/1
+ European Research Council
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- Funder identifier:
- https://ror.org/0472cxd90
- Grant:
- ERC-AdG-885414
- 101167287
- 101040760
+ United States Department of Energy
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- Funder identifier:
- https://ror.org/01bj3aw27
- Grant:
- DE-SC0011941
+ Ministero dell'Istruzione e del Merito
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- Funder identifier:
- https://ror.org/01ehyh486
- Grant:
- 20223ANFHR
- Publisher:
- American Physical Society
- Journal:
- Physical Review D (particles, fields, gravitation, and cosmology) More from this journal
- Volume:
- 113
- Issue:
- 8
- Article number:
- 85011
- Publication date:
- 2026-04-15
- Acceptance date:
- 2026-03-04
- DOI:
- EISSN:
-
2470-0029
- ISSN:
-
2470-0010
- Language:
-
English
- Pubs id:
-
2409898
- Local pid:
-
pubs:2409898
- Source identifiers:
-
W7133529456
- Deposit date:
-
2026-06-04
- ARK identifier:
Terms of use
- Copyright holder:
- American Physical Society
- Copyright date:
- 2026
- Rights statement:
- © 2026 American Physical Society. All rights reserved.
- Notes:
- The author accepted manuscript (AAM) of this paper has been made available under the University of Oxford's Open Access Publications Policy, and a CC BY public copyright licence has been applied.
- Licence:
- CC Attribution (CC BY)
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