885 research outputs found
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
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
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
Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins
We present the first analytical inspiral-merger-ringdown gravitational
waveforms from binary black holes (BBHs) with non-precessing spins, that is
based on a description of the late-inspiral, merger and ringdown in full
general relativity. By matching a post-Newtonian description of the inspiral to
a set of numerical-relativity simulations, we obtain a waveform family with a
conveniently small number of physical parameters. These waveforms will allow us
to detect a larger parameter space of BBH coalescence, including a considerable
fraction of precessing binaries in the comparable-mass regime, thus
significantly improving the expected detection rates.Comment: To appear in Phys. Rev. Lett. Significant new results. One figure
removed due to page limitatio
Review of the Laguerre-Gauss mode technology research program at Birmingham
Gravitational wave detectors from the advanced generation onwards are
expected to be limited in sensitivity by thermal noise of the optics, making
the reduction of this noise a key factor in the success of such detectors. A
proposed method for reducing the impact of this noise is to use higher-order
Laguerre-Gauss (LG) modes for the readout beam, as opposed to the currently
used fundamental mode. We present here a synopsis of the research program
undertaken by the University of Birmingham into the suitability of LG mode
technology for future gravitational wave detectors. This will cover our
previous and current work on this topic, from initial simulations and table-top
LG mode experiments up to implementation in a prototype scale suspended cavity
and high-power laser bench
Inspiral, merger and ringdown of unequal mass black hole binaries: a multipolar analysis
We study the inspiral, merger and ringdown of unequal mass black hole
binaries by analyzing a catalogue of numerical simulations for seven different
values of the mass ratio (from q=M2/M1=1 to q=4). We compare numerical and
Post-Newtonian results by projecting the waveforms onto spin-weighted spherical
harmonics, characterized by angular indices (l,m). We find that the
Post-Newtonian equations predict remarkably well the relation between the wave
amplitude and the orbital frequency for each (l,m), and that the convergence of
the Post-Newtonian series to the numerical results is non-monotonic. To leading
order the total energy emitted in the merger phase scales like eta^2 and the
spin of the final black hole scales like eta, where eta=q/(1+q)^2 is the
symmetric mass ratio. We study the multipolar distribution of the radiation,
finding that odd-l multipoles are suppressed in the equal mass limit. Higher
multipoles carry a larger fraction of the total energy as q increases. We
introduce and compare three different definitions for the ringdown starting
time. Applying linear estimation methods (the so-called Prony methods) to the
ringdown phase, we find resolution-dependent time variations in the fitted
parameters of the final black hole. By cross-correlating information from
different multipoles we show that ringdown fits can be used to obtain precise
estimates of the mass and spin of the final black hole, which are in remarkable
agreement with energy and angular momentum balance calculations.Comment: 51 pages, 28 figures, 16 tables. Many improvements throughout the
text in response to the referee report. The calculation of multipolar
components in Appendix A now uses slightly different conventions. Matches
version in press in PR
Are moving punctures equivalent to moving black holes?
When simulating the inspiral and coalescence of a binary black-hole system,
special care needs to be taken in handling the singularities. Two main
techniques are used in numerical-relativity simulations: A first and more
traditional one ``excises'' a spatial neighbourhood of the singularity from the
numerical grid on each spacelike hypersurface. A second and more recent one,
instead, begins with a ``puncture'' solution and then evolves the full
3-metric, including the singular point. In the continuum limit, excision is
justified by the light-cone structure of the Einstein equations and, in
practice, can give accurate numerical solutions when suitable discretizations
are used. However, because the field variables are non-differentiable at the
puncture, there is no proof that the moving-punctures technique is correct,
particularly in the discrete case. To investigate this question we use both
techniques to evolve a binary system of equal-mass non-spinning black holes. We
compare the evolution of two curvature 4-scalars with proper time along the
invariantly-defined worldline midway between the two black holes, using
Richardson extrapolation to reduce the influence of finite-difference
truncation errors. We find that the excision and moving-punctures evolutions
produce the same invariants along that worldline, and thus the same spacetimes
throughout that worldline's causal past. This provides convincing evidence that
moving-punctures are indeed equivalent to moving black holes.Comment: 4 pages, 3 eps color figures; v2 = major revisions to introduction &
conclusions based on referee comments, but no change in analysis or result
Formulations of the 3+1 evolution equations in curvilinear coordinates
Following Brown, in this paper we give an overview of how to modify standard
hyperbolic formulations of the 3+1 evolution equations of General Relativity in
such a way that all auxiliary quantities are true tensors, thus allowing for
these formulations to be used with curvilinear sets of coordinates such as
spherical or cylindrical coordinates. After considering the general case for
both the Nagy-Ortiz-Reula (NOR) and the Baumgarte-Shapiro-Shibata-Nakamura
(BSSN) formulations, we specialize to the case of spherical symmetry and also
discuss the issue of regularity at the origin. Finally, we show some numerical
examples of the modified BSSN formulation at work in spherical symmetry.Comment: 19 pages, 12 figure
Conformally flat black hole initial data, with one cylindrical end
We give a complete analytical proof of existence and uniqueness of
extreme-like black hole initial data for Einstein equations, which possess a
cilindrical end, analogous to extreme Kerr, extreme Reissner Nordstrom, and
extreme Bowen-York's initial data. This extends and refines a previous result
\cite{dain-gabach09} to a general case of conformally flat, maximal initial
data with angular momentum, linear momentum and matter.Comment: Minor changes and formula (21) revised according to the published
version in Class. Quantum Grav. (2010). Results unchange
Complete phenomenological gravitational waveforms from spinning coalescing binaries
The quest for gravitational waves from coalescing binaries is customarily
performed by the LIGO-Virgo collaboration via matched filtering, which requires
a detailed knowledge of the signal. Complete analytical coalescence waveforms
are currently available only for the non-precessing binary systems. In this
paper we introduce complete phenomenological waveforms for the dominant
quadrupolar mode of generically spinning systems. These waveforms are
constructed by bridging the gap between the analytically known inspiral phase,
described by spin Taylor (T4) approximants in the restricted waveform
approximation, and the ring-down phase through a phenomenological intermediate
phase, calibrated by comparison with specific, numerically generated waveforms,
describing equal mass systems with dimension-less spin magnitudes equal to 0.6.
The overlap integral between numerical and phenomenological waveforms ranges
between 0.95 and 0.99.Comment: Proceeding for the GWDAW-14 conference. Added reference in v
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