37,681 research outputs found
Bowen-York trumpet data and black-hole simulations
The most popular method to construct initial data for black-hole-binary
simulations is the puncture method, in which compactified wormholes are given
linear and angular momentum via the Bowen-York extrinsic curvature. When these
data are evolved, they quickly approach a ``trumpet'' topology, suggesting that
it would be preferable to use data that are in trumpet form from the outset. To
achieve this, we extend the puncture method to allow the construction of
Bowen-York trumpets, including an outline of an existence and uniqueness proof
of the solutions. We construct boosted, spinning and binary Bowen-York puncture
trumpets using a single-domain pseudospectral elliptic solver, and evolve the
binary data and compare with standard wormhole-data results. We also show that
for boosted trumpets the black-hole mass can be prescribed {\it a priori},
without recourse to the iterative procedure that is necessary for wormhole
data.Comment: 15 pages, 14 figures. Published versio
Binary-black-hole initial data with nearly-extremal spins
There is a significant possibility that astrophysical black holes with
nearly-extremal spins exist. Numerical simulations of such systems require
suitable initial data. In this paper, we examine three methods of constructing
binary-black-hole initial data, focusing on their ability to generate black
holes with nearly-extremal spins: (i) Bowen-York initial data, including
standard puncture data (based on conformal flatness and Bowen-York extrinsic
curvature), (ii) standard quasi-equilibrium initial data (based on the
extended-conformal-thin-sandwich equations, conformal flatness, and maximal
slicing), and (iii) quasi-equilibrium data based on the superposition of
Kerr-Schild metrics. We find that the two conformally-flat methods (i) and (ii)
perform similarly, with spins up to about 0.99 obtainable at the initial time.
However, in an evolution, we expect the spin to quickly relax to a
significantly smaller value around 0.93 as the initial geometry relaxes. For
quasi-equilibrium superposed Kerr-Schild (SKS) data [method (iii)], we
construct initial data with \emph{initial} spins as large as 0.9997. We evolve
SKS data sets with spins of 0.93 and 0.97 and find that the spin drops by only
a few parts in 10^4 during the initial relaxation; therefore, we expect that
SKS initial data will allow evolutions of binary black holes with relaxed spins
above 0.99. [Abstract abbreviated; full abstract also mentions several
secondary results.
Alternatives to standard puncture initial data for binary black hole evolution
Standard puncture initial data have been widely used for numerical binary
black hole evolutions despite their shortcomings, most notably the inherent
lack of gravitational radiation at the initial time that is later followed by a
burst of spurious radiation. We study the evolution of three alternative
initial data schemes. Two of the three alternatives are based on post-Newtonian
expansions that contain realistic gravitational waves. The first scheme is
based on a second-order post-Newtonian expansion in Arnowitt, Deser, and Misner
transverse-traceless (ADMTT) gauge that has been resummed to approach standard
puncture data at the black holes. The second scheme is based on asymptotic
matching of the 4-metrics of two tidally perturbed Schwarzschild solutions to a
first-order post-Newtonian expansion in ADMTT gauge away from the black holes.
The final alternative is obtained through asymptotic matching of the 4-metrics
of two tidally perturbed Schwarzschild solutions to a second-order
post-Newtonian expansion in harmonic gauge away from the black holes. When
evolved, the second scheme fails to produce quasicircular orbits (and instead
leads to a nearly head-on collision). This failure can be traced back to
inaccuracies in the extrinsic curvature due to low order matching. More
encouraging is that the latter two alternatives lead to quasicircular orbits
and show gravitational radiation from the onset of the evolution, as well as a
reduction of spurious radiation. Current deficiencies compared to standard
punctures data include more eccentric trajectories during the inspiral and
larger constraint violations, since the alternative data sets are only
approximate solutions of Einstein's equations. The eccentricity problem can be
ameliorated by adjusting the initial momentum parameters.Comment: 11 pages, 11 figures, 1 appendix, typos corrected, removed duplicate
reference, matches published versio
Conformal thin-sandwich puncture initial data for boosted black holes
We apply the puncture approach to conformal thin-sandwich black-hole initial
data. We solve numerically the conformal thin-sandwich puncture (CTSP)
equations for a single black hole with non-zero linear momentum. We show that
conformally flat solutions for a boosted black hole have the same maximum
gravitational radiation content as the corresponding Bowen-York solution in the
conformal transverse-traceless decomposition. We find that the physical
properties of these data are independent of the free slicing parameter.Comment: 12 pages, 11 figure
A single-domain spectral method for black hole puncture data
We calculate puncture initial data corresponding to both single and binary
black hole solutions of the constraint equations by means of a pseudo-spectral
method applied in a single spatial domain. Introducing appropriate coordinates,
these methods exhibit rapid convergence of the conformal factor and lead to
highly accurate solutions. As an application we investigate small mass ratios
of binary black holes and compare these with the corresponding test mass limit
that we obtain through a semi-analytical limiting procedure. In particular, we
compare the binding energy of puncture data in this limit with that of a test
particle in the Schwarzschild spacetime and find that it deviates by 50% from
the Schwarzschild result at the innermost stable circular orbit of
Schwarzschild, if the ADM mass at each puncture is used to define the local
black hole masses.Comment: 13 pages, 6 figures; published version with one important change, see
Fig. 4 and the corresponding changes to the tex
Quasi-circular orbits of conformal thin-sandwich puncture binary black holes
I construct initial data for equal-mass irrotational binary black holes using
the conformal thin-sandwich puncture (CTSP) approach. I locate quasi-circular
orbits using the effective-potential method, and estimate the location of the
innermost stable circular orbit (ISCO). The ISCO prediction is consistent with
results for conformal thin-sandwich data produced using excision techniques.
These results also show that the ISCOs predicted by the effective-potential and
ADM-Komar mass-comparison methods agree for conformal thin-sandwich data, just
as they did for Bowen-York data.Comment: 7 pages, 1 figure. Added discussion of the Komar mass, and slight
modifications for published versio
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