2,162 research outputs found
The imposition of Cauchy data to the Teukolsky equation III: The rotating case
We solve the problem of expressing the Weyl scalars that describe
gravitational perturbations of a Kerr black hole in terms of Cauchy data. To do
so we use geometrical identities (like the Gauss-Codazzi relations) as well as
Einstein equations. We are able to explicitly express and as functions only of the extrinsic curvature and the three-metric (and
geometrical objects built out of it) of a generic spacelike slice of the
spacetime. These results provide the link between initial data and to
be evolved by the Teukolsky equation, and can be used to compute the
gravitational radiation generated by two orbiting black holes in the close
limit approximation. They can also be used to extract waveforms from spacetimes
completely generated by numerical methods.Comment: 5 pages, REVTEX, no 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
Inspiralling black holes: the close limit
Using several approximations, we calculate an estimate of the gravitational
radiation emitted when two equal mass black holes coalesce at the end of their
binary inspiral. We find that about 1% of the mass energy of the pair will
emerge as gravitational waves during the final ringdown and a negligible
fraction of the angular momentum will be radiated.Comment: 4 pages, RevTeX, 2 figure
Reconstruction of Black Hole Metric Perturbations from Weyl Curvature II: The Regge-Wheeler gauge
Perturbation theory of rotating black holes is described in terms of the Weyl
scalars and ; each satisfying the Teukolsky's complex master
wave equation with spin , and respectively representing outgoing and
ingoing radiation. We explicitly construct the metric perturbations out of
these Weyl scalars in the Regge-Wheeler gauge in the nonrotating limit. We
propose a generalization of the Regge-Wheeler gauge for Kerr background in the
Newman-Penrose language, and discuss the approach for building up the perturbed
spacetime of a rotating black hole. We also provide both-way relationships
between waveforms defined in the metric and curvature approaches in the time
domain, also known as the (inverse-) Chandrasekhar transformations, generalized
to include matter.Comment: 22 pages, no 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
On the Sandpile group of the cone of a graph
In this article, we give a partial description of the sandpile group of the
cone of the cartesian product of graphs in function of the sandpile group of
the cone of their factors. Also, we introduce the concept of uniform
homomorphism of graphs and prove that every surjective uniform homomorphism of
graphs induces an injective homomorphism between their sandpile groups. As an
application of these result we obtain an explicit description of a set of
generators of the sandpile group of the cone of the hypercube of dimension d.Comment: 20 pages, 11 figures. The title was changed, other impruvements were
made throughout the article. To appear in Linear Algebra and Its Application
Spread of metals through an invertebrate food chain as influenced by a plant that hyperaccumulates nickel
Hyperaccumulation of metals in the shoot
system of plants is uncommon, yet taxonomically and geographically
widespread. It may have a variety of functions,
including defense against herbivores. This study investigated
the effects of hyperaccumulation on metal concentrations
across trophic levels. We collected plant material,
soil, and invertebrates from Portuguese serpentine outcrops
whose vegetation is dominated by the nickel hyperaccumulator
Alyssum pintodasilvae. Samples were analyzed for
nickel, chromium, and cobalt. Grasshoppers, spiders, and
other invertebrates collected from sites where A. pintodasilvae
was common had significantly elevated concentrations
of nickel, compared to nearby sites where this hyperaccumulator
was not found. Chromium and cobalt, occurring in
high concentrations in the serpentine soil but not accumulated
by A. pintodasilvae, were not elevated in the invertebrates.
Therefore, it appears likely that a flux of nickel to
herbivore and carnivore trophic levels is specifically facilitated
by the presence of plants that hyperaccumulate this
metal. The results may be relevant to the development of
phytoremediation and phytomining technologies, which use
plants to extract metals from the soil
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
The Lazarus project: A pragmatic approach to binary black hole evolutions
We present a detailed description of techniques developed to combine 3D
numerical simulations and, subsequently, a single black hole close-limit
approximation. This method has made it possible to compute the first complete
waveforms covering the post-orbital dynamics of a binary black hole system with
the numerical simulation covering the essential non-linear interaction before
the close limit becomes applicable for the late time dynamics. To determine
when close-limit perturbation theory is applicable we apply a combination of
invariant a priori estimates and a posteriori consistency checks of the
robustness of our results against exchange of linear and non-linear treatments
near the interface. Once the numerically modeled binary system reaches a regime
that can be treated as perturbations of the Kerr spacetime, we must
approximately relate the numerical coordinates to the perturbative background
coordinates. We also perform a rotation of a numerically defined tetrad to
asymptotically reproduce the tetrad required in the perturbative treatment. We
can then produce numerical Cauchy data for the close-limit evolution in the
form of the Weyl scalar and its time derivative
with both objects being first order coordinate and tetrad invariant. The
Teukolsky equation in Boyer-Lindquist coordinates is adopted to further
continue the evolution. To illustrate the application of these techniques we
evolve a single Kerr hole and compute the spurious radiation as a measure of
the error of the whole procedure. We also briefly discuss the extension of the
project to make use of improved full numerical evolutions and outline the
approach to a full understanding of astrophysical black hole binary systems
which we can now pursue.Comment: New typos found in the version appeared in PRD. (Mostly found and
collected by Bernard Kelly
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
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