3 research outputs found
Intermediate behavior of Kerr tails
The numerical investigation of wave propagation in the asymptotic domain of
Kerr spacetime has only recently been possible thanks to the construction of
suitable hyperboloidal coordinates. The asymptotics revealed an apparent puzzle
in the decay rates of scalar fields: the late-time rates seemed to depend on
whether finite distance observers are in the strong field domain or far away
from the rotating black hole, an apparent phenomenon dubbed "splitting". We
discuss far-field "splitting" in the full field and near-horizon "splitting" in
certain projected modes using horizon-penetrating, hyperboloidal coordinates.
For either case we propose an explanation to the cause of the "splitting"
behavior, and we determine uniquely decay rates that previous studies found to
be ambiguous or immeasurable. The far-field "splitting" is explained by
competition between projected modes. The near-horizon "splitting" is due to
excitation of lower multipole modes that back excite the multipole mode for
which "splitting" is observed. In both cases "splitting" is an intermediate
effect, such that asymptotically in time strong field rates are valid at all
finite distances. At any finite time, however, there are three domains with
different decay rates whose boundaries move outwards during evolution. We then
propose a formula for the decay rate of tails that takes into account the
inter--mode excitation effect that we study.Comment: 16 page
Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration
The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a
joint effort between members of the numerical relativity, analytical relativity
and gravitational-wave data analysis communities. The goal of the NRAR
collaboration is to produce numerical-relativity simulations of compact
binaries and use them to develop accurate analytical templates for the
LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and
extracting astrophysical information from them. We describe the results of the
first stage of the NRAR project, which focused on producing an initial set of
numerical waveforms from binary black holes with moderate mass ratios and
spins, as well as one non-spinning binary configuration which has a mass ratio
of 10. All of the numerical waveforms are analysed in a uniform and consistent
manner, with numerical errors evaluated using an analysis code created by
members of the NRAR collaboration. We compare previously-calibrated,
non-precessing analytical waveforms, notably the effective-one-body (EOB) and
phenomenological template families, to the newly-produced numerical waveforms.
We find that when the binary's total mass is ~100-200 solar masses, current EOB
and phenomenological models of spinning, non-precessing binary waveforms have
overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary
numerical waveforms with mass ratios <= 4, when maximizing over binary
parameters. This implies that the loss of event rate due to modelling error is
below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to
five non-spinning waveforms with mass ratio smaller than 6 have overlaps above
99.7% with the numerical waveform with a mass ratio of 10, without even
maximizing on the binary parameters.Comment: 51 pages, 10 figures; published versio
Hyperboloidal foliations and scri-fixing
We discuss a gauge choice which allows us to avoid the introduction of
artificial timelike outer boundaries in numerical studies of test fields based
on a 3+1 decomposition of asymptotically flat background spacetimes. The main
idea is to include null infinity in the computational domain by conformally
compactifying the metric on hyperboloidal foliations and fixing the spatial
coordinate location of null infinity, i.e. scri-fixing. We construct such
coordinates explicitly on Minkowski, Schwarzschild and Kerr spacetimes.Comment: 14 pages, 14 figures. Published versio