223 research outputs found
Boundary conditions in linearized harmonic gravity
We investigate the initial-boundary value problem for linearized
gravitational theory in harmonic coordinates. Rigorous techniques for
hyperbolic systems are applied to establish well-posedness for various
reductions of the system into a set of six wave equations. The results are used
to formulate computational algorithms for Cauchy evolution in a 3-dimensional
bounded domain. Numerical codes based upon these algorithms are shown to
satisfy tests of robust stability for random constraint violating initial data
and random boundary data; and shown to give excellent performance for the
evolution of typical physical data. The results are obtained for plane
boundaries as well as piecewise cubic spherical boundaries cut out of a
Cartesian grid.Comment: 22 pages, 6 Postscript figure
Some mathematical problems in numerical relativity
The main goal of numerical relativity is the long time simulation of highly
nonlinear spacetimes that cannot be treated by perturbation theory. This
involves analytic, computational and physical issues. At present, the major
impasses to achieving global simulations of physical usefulness are of an
analytic/computational nature. We present here some examples of how analytic
insight can lend useful guidance for the improvement of numerical approaches.Comment: 17 pages, 12 graphs (eps format
Lattice Boltzmann Approach to Viscous Flows Between Parallel Plates
Four different kinds of laminar flows between two parallel plates are
investigated using the Lattice Boltzmann Method (LBM). The LBM accuracy is
estimated in two cases using numerical fits of the parabolic velocity profiles
and the kinetic energy decay curves, respectively. The error relative to the
analytical kinematic viscosity values was found to be less than one percent in
both cases. The LBM results for the unsteady development of the flow when one
plate is brought suddenly at a constant velocity, are found in excellent
agreement with the analytical solution. Because the classical Schlichting's
approximate solution for the entrance--region flow is not valid for small
Reynolds numbers, a Finite Element Method solution was used in order to check
the accuracy of the LBM results
Accurate gravitational waveforms for binary-black-hole mergers with nearly extremal spins
Motivated by the possibility of observing gravitational waves from merging
black holes whose spins are nearly extremal (i.e., 1 in dimensionless units),
we present numerical waveforms from simulations of merging black holes with the
highest spins simulated to date: (1) a 25.5-orbit inspiral, merger, and
ringdown of two holes with equal masses and spins of magnitude 0.97 aligned
with the orbital angular momentum; and (2) a previously reported 12.5-orbit
inspiral, merger, and ringdown of two holes with equal masses and spins of
magnitude 0.95 anti-aligned with the orbital angular momentum. First, we
consider the horizon mass and spin evolution of the new aligned-spin
simulation. During the inspiral, the horizon area and spin evolve in remarkably
close agreement with Alvi's analytic predictions, and the remnant hole's final
spin agrees reasonably well with several analytic predictions. We also find
that the total energy emitted by a real astrophysical system with these
parameters---almost all of which is radiated during the time included in this
simulation---would be 10.952% of the initial mass at infinite separation.
Second, we consider the gravitational waveforms for both simulations. After
estimating their uncertainties, we compare the waveforms to several
post-Newtonian approximants, finding significant disagreement well before
merger, although the phase of the TaylorT4 approximant happens to agree
remarkably well with the numerical prediction in the aligned-spin case. We find
that the post-Newtonian waveforms have sufficient uncertainty that hybridized
waveforms will require far longer numerical simulations (in the absence of
improved post-Newtonian waveforms) for accurate parameter estimation of
low-mass binary systems.Comment: 17 pages, 7 figures, submitted to Classical and Quantum Gravit
A sparse representation of gravitational waves from precessing compact binaries
Many relevant applications in gravitational wave physics share a significant
common problem: the seven-dimensional parameter space of gravitational
waveforms from precessing compact binary inspirals and coalescences is large
enough to prohibit covering the space of waveforms with sufficient density. We
find that by using the reduced basis method together with a parametrization of
waveforms based on their phase and precession, we can construct ultra-compact
yet high-accuracy representations of this large space. As a demonstration, we
show that less than judiciously chosen precessing inspiral waveforms are
needed for cycles, mass ratios from to and spin magnitudes . In fact, using only the first reduced basis waveforms yields a
maximum mismatch of over the whole range of considered parameters. We
test whether the parameters selected from the inspiral regime result in an
accurate reduced basis when including merger and ringdown; we find that this is
indeed the case in the context of a non-precessing effective-one-body model.
This evidence suggests that as few as numerical simulations of
binary black hole coalescences may accurately represent the seven-dimensional
parameter space of precession waveforms for the considered ranges.Comment: 5 pages, 3 figures. The parameters selected for the basis of
precessing waveforms can be found in the source file
Spin Diagrams for Equal-Mass Black-Hole Binaries with Aligned Spins
Binary black-hole systems with spins aligned with the orbital angular
momentum are of special interest as they may be the preferred end-state of the
inspiral of generic supermassive binary black-hole systems. In view of this, we
have computed the inspiral and merger of a large set of binary systems of
equal-mass black holes with spins aligned with the orbital angular momentum but
otherwise arbitrary. By least-square fitting the results of these simulations
we have constructed two "spin diagrams" which provide straightforward
information about the recoil velocity |v_kick| and the final black-hole spin
a_fin in terms of the dimensionless spins a_1 and a_2 of the two initial black
holes. Overall they suggest a maximum recoil velocity of |v_kick|=441.94 km/s,
and minimum and maximum final spins a_fin=0.3471 and a_fin=0.9591,
respectively.Comment: 4 pages, 3 figs; small changes matching published versio
Black hole-neutron star mergers for 10 solar mass black holes
General relativistic simulations of black hole-neutron star mergers have
currently been limited to low-mass black holes (less than 7 solar mass), even
though population synthesis models indicate that a majority of mergers might
involve more massive black holes (10 solar mass or more). We present the first
general relativistic simulations of black hole-neutron star mergers with 10
solar mass black holes. For massive black holes, the tidal forces acting on the
neutron star are usually too weak to disrupt the star before it reaches the
innermost stable circular orbit of the black hole. Varying the spin of the
black hole in the range a/M = 0.5-0.9, we find that mergers result in the
disruption of the star and the formation of a massive accretion disk only for
large spins a/M>0.7-0.9. From these results, we obtain updated constraints on
the ability of BHNS mergers to be the progenitors of short gamma-ray bursts as
a function of the mass and spin of the black hole. We also discuss the
dependence of the gravitational wave signal on the black hole parameters, and
provide waveforms and spectra from simulations beginning 7-8 orbits before
merger.Comment: 11 pages, 11 figures - Updated to match published versio
Initial data for black hole-neutron star binaries, with rotating stars
The coalescence of a neutron star with a black hole is a primary science
target of ground-based gravitational wave detectors. Constraining or measuring
the neutron star spin directly from gravitational wave observations requires
knowledge of the dependence of the emission properties of these systems on the
neutron star spin. This paper lays foundations for this task, by developing a
numerical method to construct initial data for black hole--neutron star
binaries with arbitrary spin on the neutron star. We demonstrate the robustness
of the code by constructing initial-data sets in large regions of the parameter
space. In addition to varying the neutron star spin-magnitude and
spin-direction, we also explore neutron star compactness, mass-ratio, black
hole spin, and black hole spin-direction. Specifically, we are able to
construct initial data sets with neutron stars spinning near centrifugal
break-up, and with black hole spins as large as .Comment: 25 pages, 12 figure
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