652 research outputs found
Binary black holes on a budget: Simulations using workstations
Binary black hole simulations have traditionally been computationally very
expensive: current simulations are performed in supercomputers involving dozens
if not hundreds of processors, thus systematic studies of the parameter space
of binary black hole encounters still seem prohibitive with current technology.
Here we show how the multi-layered refinement level code BAM can be used on
dual processor workstations to simulate certain binary black hole systems. BAM,
based on the moving punctures method, provides grid structures composed of
boxes of increasing resolution near the center of the grid. In the case of
binaries, the highest resolution boxes are placed around each black hole and
they track them in their orbits until the final merger when a single set of
levels surrounds the black hole remnant. This is particularly useful when
simulating spinning black holes since the gravitational fields gradients are
larger. We present simulations of binaries with equal mass black holes with
spins parallel to the binary axis and intrinsic magnitude of S/m^2= 0.75. Our
results compare favorably to those of previous simulations of this particular
system. We show that the moving punctures method produces stable simulations at
maximum spatial resolutions up to M/160 and for durations of up to the
equivalent of 20 orbital periods.Comment: 20 pages, 8 figures. Final version, to appear in a special issue of
Class. Quantum Grav. based on the New Frontiers in Numerical Relativity
Conference, Golm, July 200
A new numerical method to construct binary neutron star initial data
We present a new numerical method for the generation of binary neutron star
initial data using a method along the lines of the the Wilson-Mathews or the
closely related conformal thin sandwich approach. Our method uses six different
computational domains, which include spatial infinity. Each domain has its own
coordinates which are chosen such that the star surfaces always coincide with
domain boundaries. These properties facilitate the imposition of boundary
conditions. Since all our fields are smooth inside each domain, we are able to
use an efficient pseudospectral method to solve the elliptic equations
associated with the conformal thin sandwich approach. Currently we have
implemented corotating configurations with arbitrary mass ratios, but an
extension to arbitrary spins is possible. The main purpose of this paper is to
introduce our new method and to test our code for several different
configurations.Comment: 18 pages, 8 figures, 1 tabl
Black hole puncture initial data with realistic gravitational wave content
We present improved post-Newtonian-inspired initial data for non-spinning
black-hole binaries, suitable for numerical evolution with punctures. We
revisit the work of Tichy et al. [W. Tichy, B. Bruegmann, M. Campanelli, and P.
Diener, Phys. Rev. D 67, 064008 (2003)], explicitly calculating the remaining
integral terms. These terms improve accuracy in the far zone and, for the first
time, include realistic gravitational waves in the initial data. We investigate
the behavior of these data both at the center of mass and in the far zone,
demonstrating agreement of the transverse-traceless parts of the new metric
with quadrupole-approximation waveforms. These data can be used for numerical
evolutions, enabling a direct connection between the merger waveforms and the
post-Newtonian inspiral waveforms.Comment: 13 pages, 7 figures; replaced with published versio
Elliptica: a new pseudo-spectral code for the construction of initial data
Numerical studies of the dynamics of gravitational systems, e.g., black hole-neutron star systems, require physical and constraint-satisfying initial data. In this article, we present the newly developed pseudo-spectral code Elliptica, an infrastructure for construction of initial data for various binary and single gravitational systems of all kinds. The elliptic equations under consideration are solved on a single spatial hypersurface of the spacetime manifold. Using coordinate maps, the hypersurface is covered by patches whose boundaries can adapt to the surface of the compact objects. To solve elliptic equations with arbitrary boundary condition, Elliptica deploys a Schur complement domain decomposition method with a direct solver. In this version, we use cubed sphere coordinate maps and the fields are expanded using Chebyshev polynomials of the first kind. Here, we explain the building blocks of Elliptica and the initial data construction algorithm for a black hole-neutron star binary system. We perform convergence tests and evolve the data to validate our results. Within our framework, the neutron star can reach spin values close to breakup with arbitrary direction, while the black hole can have arbitrary spin with dimensionless spin magnitude
BSSN in Spherical Symmetry
The BSSN (Baumgarte-Shapiro-Shibata-Nakamura) formulation of the Einstein
evolution equations is written in spherical symmetry. These equations can be
used to address a number of technical and conceptual issues in numerical
relativity in the context of a single Schwarzschild black hole. One of the
benefits of spherical symmetry is that the numerical grid points can be tracked
on a Kruskal--Szekeres diagram. Boundary conditions suitable for puncture
evolution of a Schwarzschild black hole are presented. Several results are
shown for puncture evolution using a fourth--order finite difference
implementation of the equations.Comment: This is the final version to be published in CQG. It contains much
more information and detail than the original versio
Gauge conditions for binary black hole puncture data based on an approximate helical Killing vector
We show that puncture data for quasicircular binary black hole orbits allow a
special gauge choice that realizes some of the necessary conditions for the
existence of an approximate helical Killing vector field. Introducing free
parameters for the lapse at the punctures we can satisfy the condition that the
Komar and ADM mass agree at spatial infinity. Several other conditions for an
approximate Killing vector are then automatically satisfied, and the 3-metric
evolves on a timescale smaller than the orbital timescale. The time derivative
of the extrinsic curvature however remains significant. Nevertheless,
quasicircular puncture data are not as far from possessing a helical Killing
vector as one might have expected.Comment: 11 pages, 6 figures, 2 table
Beyond the Bowen-York extrinsic curvature for spinning black holes
It is well-known that Bowen-York initial data contain spurious radiation.
Although this ``junk'' radiation has been seen to be small for non-spinning
black-hole binaries in circular orbit, its magnitude increases when the black
holes are given spin. It is possible to reduce the spurious radiation by
applying the puncture approach to multiple Kerr black holes, as we demonstrate
for examples of head-on collisions of equal-mass black-hole binaries.Comment: 10 pages, 2 figures, submitted to special "New Frontiers in Numerical
Relativity" issue of Classical and Quantum Gravit
Asymptotically Matched Spacetime Metric for Non-Precessing, Spinning Black Hole Binaries
We construct a closed-form, fully analytical 4-metric that approximately
represents the spacetime evolution of non-precessing, spinning black hole
binaries from infinite separations up to a few orbits prior to merger. We
employ the technique of asymptotic matching to join a perturbed Kerr metric in
the neighborhood of each spinning black hole to a near-zone, post-Newtonian
metric farther out. The latter is already naturally matched to a far-zone,
post-Minkowskian metric that accounts for full temporal retardation. The result
is a 4-metric that is approximately valid everywhere in space and in a small
bundle of spatial hypersurfaces. We here restrict our attention to quasi-
circular orbits, but the method is valid for any orbital motion or physical
scenario, provided an overlapping region of validity or buffer zone exists. A
simple extension of such a metric will allow for future studies of the
accretion disk and jet dynamics around spinning back hole binaries
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