23,984 research outputs found
A time-domain fourth-order-convergent numerical algorithm to integrate black hole perturbations in the extreme-mass-ratio limit
We obtain a fourth order accurate numerical algorithm to integrate the
Zerilli and Regge-Wheeler wave equations, describing perturbations of
nonrotating black holes, with source terms due to an orbiting particle. Those
source terms contain the Dirac's delta and its first derivative. We also
re-derive the source of the Zerilli and Regge-Wheeler equations for more
convenient definitions of the waveforms, that allow direct metric
reconstruction (in the Regge-Wheeler gauge).Comment: 30 pages, 12 figure
Gravitational waves from black hole collisions via an eclectic approach
We present the first results in a new program intended to make the best use
of all available technologies to provide an effective understanding of waves
from inspiralling black hole binaries in time for imminent observations. In
particular, we address the problem of combining the close-limit approximation
describing ringing black holes and full numerical relativity, required for
essentially nonlinear interactions. We demonstrate the effectiveness of our
approach using general methods for a model problem, the head-on collision of
black holes. Our method allows a more direct physical understanding of these
collisions indicating clearly when non-linear methods are important. The
success of this method supports our expectation that this unified approach will
be able to provide astrophysically relevant results for black hole binaries in
time to assist gravitational wave observations.Comment: 4 pages, 3 eps figures, Revte
Four-nucleon scattering: Ab initio calculations in momentum space
The four-body equations of Alt, Grassberger and Sandhas are solved for \nH
scattering at energies below three-body breakup threshold using various
realistic interactions including one derived from chiral perturbation theory.
After partial wave decomposition the equations are three-variable integral
equations that are solved numerically without any approximations beyond the
usual discretization of continuum variables on a finite momentum mesh. Large
number of two-, three- and four-nucleon partial waves are considered until the
convergence of the observables is obtained. The total \nH cross section data
in the resonance region is not described by the calculations which confirms
previous findings by other groups. Nevertheless the numbers we get are slightly
higher and closer to the data than previously found and depend on the choice of
the two-nucleon potential. Correlations between the deficiency in \nd
elastic scattering and the total \nH cross section are studied.Comment: Corrected Eq. (10
Accurate black hole evolutions by fourth-order numerical relativity
We present techniques for successfully performing numerical relativity
simulations of binary black holes with fourth-order accuracy. Our simulations
are based on a new coding framework which currently supports higher order
finite differencing for the BSSN formulation of Einstein's equations, but which
is designed to be readily applicable to a broad class of formulations. We apply
our techniques to a standard set of numerical relativity test problems,
demonstrating the fourth-order accuracy of the solutions. Finally we apply our
approach to binary black hole head-on collisions, calculating the waveforms of
gravitational radiation generated and demonstrating significant improvements in
waveform accuracy over second-order methods with typically achievable numerical
resolution.Comment: 17 pages, 25 figure
Placing regenerators in optical networks to satisfy multiple sets of requests.
The placement of regenerators in optical networks has become an active area of research during the last years. Given a set of lightpaths in a network G and a positive integer d, regenerators must be placed in such a way that in any lightpath there are no more than d hops without meeting a regenerator. While most of the research has focused on heuristics and simulations, the first theoretical study of the problem has been recently provided in [10], where the considered cost function is the number of locations in the network hosting regenerators. Nevertheless, in many situations a more accurate estimation of the real cost of the network is given by the total number of regenerators placed at the nodes, and this is the cost function we consider. Furthermore, in our model we assume that we are given a finite set of p possible traffic patterns (each given by a set of lightpaths), and our objective is to place the minimum number of regenerators at the nodes so that each of the traffic patterns is satisfied. While this problem can be easily solved when d = 1 or p = 1, we prove that for any fixed d,p ≥ 2 it does not admit a PTASUnknown control sequence '\textsc', even if G has maximum degree at most 3 and the lightpaths have length O(d)(d). We complement this hardness result with a constant-factor approximation algorithm with ratio ln (d ·p). We then study the case where G is a path, proving that the problem is NP-hard for any d,p ≥ 2, even if there are two edges of the path such that any lightpath uses at least one of them. Interestingly, we show that the problem is polynomial-time solvable in paths when all the lightpaths share the first edge of the path, as well as when the number of lightpaths sharing an edge is bounded. Finally, we generalize our model in two natural directions, which allows us to capture the model of [10] as a particular case, and we settle some questions that were left open in [10]
Seeking for toroidal event horizons from initially stationary BH configurations
We construct and evolve non-rotating vacuum initial data with a ring
singularity, based on a simple extension of the standard Brill-Lindquist
multiple black-hole initial data, and search for event horizons with spatial
slices that are toroidal when the ring radius is sufficiently large. While
evolutions of the ring singularity are not numerically feasible for large
radii, we find some evidence, based on configurations of multiple BHs arranged
in a ring, that this configuration leads to singular limit where the horizon
width has zero size, possibly indicating the presence of a naked singularity,
when the radius of the ring is sufficiently large. This is in agreement with
previous studies that have found that there is no apparent horizon surrounding
the ring singularity when the ring's radius is larger than about twice its
mass.Comment: 24 pages, 14 figure
Modeling Gravitational Recoil Using Numerical Relativity
We review the developments in modeling gravitational recoil from merging
black-hole binaries and introduce a new set of 20 simulations to test our
previously proposed empirical formula for the recoil. The configurations are
chosen to represent generic binaries with unequal masses and precessing spins.
Results of these simulations indicate that the recoil formula is accurate to
within a few km/s in the similar mass-ratio regime for the out-of-plane recoil.Comment: corrections to text, 11 pages, 1 figur
Making use of geometrical invariants in black hole collisions
We consider curvature invariants in the context of black hole collision
simulations. In particular, we propose a simple and elegant combination of the
Weyl invariants I and J, the {\sl speciality index} . In the context
of black hole perturbations provides a measure of the size of the
distortions from an ideal Kerr black hole spacetime. Explicit calculations in
well-known examples of axisymmetric black hole collisions demonstrate that this
quantity may serve as a useful tool for predicting in which cases perturbative
dynamics provide an accurate estimate of the radiation waveform and energy.
This makes particularly suited to studying the transition from
nonlinear to linear dynamics and for invariant interpretation of numerical
results.Comment: 4 pages, 3 eps figures, Revte
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