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 ${\mathcal{I}}^{+}$, 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 ${\mathcal{I}}^{+}$. 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 $1000M$ 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.

arXiv comment26 pages, 10 figures