Accurate initial data for Cauchy-characteristic evolution
Abstract
Accurate gravitational-wave (GW) templates from numerical-relativity (NR) simulations are essential for GW science. These templates are typically computed at finite radii and extrapolated to future null infinity ℐ+, the asymptotic boundary of spacetime. However, this procedure is known to not accurately capture momentum fluxes and memory effects, limiting the accuracy of waveform models and data analyses that rely on them. Cauchy-characteristic evolution (CCE) instead integrates Einstein's equations along outgoing null hypersurfaces from a Cauchy simulation's finite-radius worldtube to ℐ+. Its accuracy, though, has been limited by initial data that produce long-lived spurious transients, which contaminate several cycles of the waveform emitted by the binary coalescence. We identify incorrect initial angular coordinates as the source of these transients. We construct initial data that matches the Cauchy worldtube data through second order in the radial derivatives and solve for the angular coordinates consistent with the resulting radial profile. These improvements remove the unphysical transient: a 10% modulation of a binary black hole's (2,2) mode amplitude lasting over 1000 M disappears, and the late-time tail of a head-on black hole collision is recovered. The construction is independent of the Cauchy formulation and allows archived simulations to be reprocessed with CCE, paving the way for improved GW catalogs.
Related
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BibTeX
@misc{re2026accurate,
title = {{Accurate initial data for Cauchy-characteristic evolution}},
author = {Guido Da Re and Keefe Mitman and Leo C. Stein and Nils Deppe and Himanshu Chaudhary and Dongze Sun and Michael Boyle and Kyle C. Nelli and Mark A. Scheel and Saul A. Teukolsky},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30268},
eprint = {2610.30268},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30268},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Accurate initial data for Cauchy-characteristic evolution
AU - Guido Da Re
AU - Keefe Mitman
AU - Leo C. Stein
AU - Nils Deppe
AU - Himanshu Chaudhary
AU - Dongze Sun
AU - Michael Boyle
AU - Kyle C. Nelli
AU - Mark A. Scheel
AU - Saul A. Teukolsky
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30268
UR - https://arxiv.org/abs/2610.30268
AB - Accurate gravitational-wave (GW) templates from numerical-relativity (NR) simulations are essential for GW science. These templates are typically computed at finite radii and extrapolated to future null infinity ℐ^+, the asymptotic boundary of spacetime. However, this procedure is known to not accurately capture momentum fluxes and memory effects, limiting the accuracy of waveform models and data analyses that rely on them. Cauchy-characteristic evolution (CCE) instead integrates Einstein's equations along outgoing null hypersurfaces from a Cauchy simulation's finite-radius worldtube to ℐ^+. Its accuracy, though, has been limited by initial data that produce long-lived spurious transients, which contaminate several cycles of the waveform emitted by the binary coalescence. We identify incorrect initial angular coordinates as the source of these transients. We construct initial data that matches the Cauchy worldtube data through second order in the radial derivatives and solve for the angular coordinates consistent with the resulting radial profile. These improvements remove the unphysical transient: a 10% modulation of a binary black hole's (2,2) mode amplitude lasting over 1000 M disappears, and the late-time tail of a head-on black hole collision is recovered. The construction is independent of the Cauchy formulation and allows archived simulations to be reprocessed with CCE, paving the way for improved GW catalogs.
ER -