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General Relativity and Quantum Cosmology, gr-qc
Abstract:
(Abridged) By asymptotically matching a post-Newtonian (PN) metric to two
tidally perturbed Schwarzschild metrics, we generate approximate initial data
(in the form of a 4-metric) for a nonspinning black hole binary in a circular
orbit. We carry out this matching through O(v^4) in the binary's orbital
velocity v, so the resulting data are conformally curved. Far from the holes,
we use the appropriate PN metric that accounts for retardation, which we
construct using the highest-order PN expressions available to compute the
binary's past history. The data set's uncontrolled remainders are thus O(v^5)
throughout the timeslice; we also generate an extension to the data set that
has uncontrolled remainders of O(v^6) in the purely PN portion of the timeslice
(i.e., not too close to the holes). The resulting data are smooth, since we
join all the metrics together by smoothly interpolating between them. We
perform this interpolation using transition functions constructed to avoid
introducing excessive additional constraint violations. Due to their inclusion
of tidal deformations and outgoing radiation, these data should substantially
reduce the initial spurious ("junk") radiation observed in current simulations
that use conformally flat initial data. Such reductions in the nonphysical
components of the initial data will be necessary for simulations to achieve the
accuracy required to supply Advanced LIGO and LISA with the templates necessary
for parameter estimation.
