314 research outputs found
Why Solve the Hamiltonian Constraint in Numerical Relativity?
The indefinite sign of the Hamiltonian constraint means that solutions to
Einstein's equations must achieve a delicate balance--often among numerically
large terms that nearly cancel. If numerical errors cause a violation of the
Hamiltonian constraint, the failure of the delicate balance could lead to
qualitatively wrong behavior rather than just decreased accuracy. This issue is
different from instabilities caused by constraint-violating modes. Examples of
stable numerical simulations of collapsing cosmological spacetimes exhibiting
local mixmaster dynamics with and without Hamiltonian constraint enforcement
are presented.Comment: Submitted to a volume in honor of Michael P. Ryan, Jr. Based on talk
given at GR1
Radiative falloff in the background of rotating black hole
We study numerically the late-time tails of linearized fields with any spin
in the background of a spinning black hole. Our code is based on the
ingoing Kerr coordinates, which allow us to penetrate through the event
horizon. The late time tails are dominated by the mode with the least multipole
moment which is consistent with the equatorial symmetry of the initial
data and is equal to or greater than the least radiative mode with and the
azimuthal number .Comment: 5 pages, 4 Encapsulated PostScript figures; Accepted to Phys. Rev. D
(Rapid Communication
Radiative falloff of a scalar field in a weakly curved spacetime without symmetries
We consider a massless scalar field propagating in a weakly curved spacetime
whose metric is a solution to the linearized Einstein field equations. The
spacetime is assumed to be stationary and asymptotically flat, but no other
symmetries are imposed -- the spacetime can rotate and deviate strongly from
spherical symmetry. We prove that the late-time behavior of the scalar field is
identical to what it would be in a spherically-symmetric spacetime: it decays
in time according to an inverse power-law, with a power determined by the
angular profile of the initial wave packet (Price falloff theorem). The field's
late-time dynamics is insensitive to the nonspherical aspects of the metric,
and it is governed entirely by the spacetime's total gravitational mass; other
multipole moments, and in particular the spacetime's total angular momentum, do
not enter in the description of the field's late-time behavior. This extended
formulation of Price's falloff theorem appears to be at odds with previous
studies of radiative decay in the spacetime of a Kerr black hole. We show,
however, that the contradiction is only apparent, and that it is largely an
artifact of the Boyer-Lindquist coordinates adopted in these studies.Comment: 17 pages, RevTeX
Radiative falloff in Einstein-Straus spacetime
The Einstein-Straus spacetime describes a nonrotating black hole immersed in
a matter-dominated cosmology. It is constructed by scooping out a spherical
ball of the dust and replacing it with a vacuum region containing a black hole
of the same mass. The metric is smooth at the boundary, which is comoving with
the rest of the universe. We study the evolution of a massless scalar field in
the Einstein-Straus spacetime, with a special emphasis on its late-time
behavior. This is done by numerically integrating the scalar wave equation in a
double-null coordinate system that covers both portions (vacuum and dust) of
the spacetime. We show that the field's evolution is governed mostly by the
strong concentration of curvature near the black hole, and the discontinuity in
the dust's mass density at the boundary; these give rise to a rather complex
behavior at late times. Contrary to what it would do in an asymptotically-flat
spacetime, the field does not decay in time according to an inverse power-law.Comment: ReVTeX, 12 pages, 14 figure
Scalar wave propagation in topological black hole backgrounds
We consider the evolution of a scalar field coupled to curvature in
topological black hole spacetimes. We solve numerically the scalar wave
equation with different curvature-coupling constant and show that a rich
spectrum of wave propagation is revealed when is introduced. Relations
between quasinormal modes and the size of different topological black holes
have also been investigated.Comment: 26 pages, 18 figure
Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes
We set up the singular initial value problem for quasilinear hyperbolic
Fuchsian systems of first order and establish an existence and uniqueness
theory for this problem with smooth data and smooth coefficients (and with even
lower regularity). We apply this theory in order to show the existence of
smooth (generally not analytic) T2-symmetric solutions to the vacuum Einstein
equations, which exhibit AVTD (asymptotically velocity term dominated) behavior
in the neighborhood of their singularities and are polarized or half-polarized.Comment: 78 page
Numerical simulation of the massive scalar field evolution in the Reissner-Nordstr\"{o}m black hole background
We studied the massive scalar wave propagation in the background of
Reissner-Nordstr\"{o}m black hole by using numerical simulations. We learned
that the value plays an important role in determining the properties of
the relaxation of the perturbation. For the relaxation process
depends only on the field parameter and does not depend on the spacetime
parameters. For , the dependence of the relaxation on the black hole
parameters appears. The bigger mass of the black hole, the faster the
perturbation decays. The difference of the relaxation process caused by the
black hole charge has also been exhibited.Comment: Accepted for publication in Phys. Rev.
Wave Propagation in Gravitational Systems: Late Time Behavior
It is well-known that the dominant late time behavior of waves propagating on
a Schwarzschild spacetime is a power-law tail; tails for other spacetimes have
also been studied. This paper presents a systematic treatment of the tail
phenomenon for a broad class of models via a Green's function formalism and
establishes the following. (i) The tail is governed by a cut of the frequency
Green's function along the ~Im~ axis,
generalizing the Schwarzschild result. (ii) The dependence of the cut
is determined by the asymptotic but not the local structure of space. In
particular it is independent of the presence of a horizon, and has the same
form for the case of a star as well. (iii) Depending on the spatial
asymptotics, the late time decay is not necessarily a power law in time. The
Schwarzschild case with a power-law tail is exceptional among the class of the
potentials having a logarithmic spatial dependence. (iv) Both the amplitude and
the time dependence of the tail for a broad class of models are obtained
analytically. (v) The analytical results are in perfect agreement with
numerical calculations
The ecology of sex explains patterns of helping in arthropod societies
Authors thank the Natural Sciences and Engineering Research Council of Canada (NGD), the Clarendon Fund (NGD) and the Natural Environment Research Council (LR, NE/K009516/1; AG, NE/K009524/1) for funding.Across arthropod societies, sib-rearing (e.g. nursing or nest defence) may be provided by females, by males or by both sexes. According to Hamilton's âhaplodiploidy hypothesisâ, this diversity reflects the relatedness consequences of diploid vs. haplodiploid inheritance. However, an alternative âpreadaptation hypothesisâ instead emphasises an interplay of ecology and the co-option of ancestral, sexually dimorphic traits for sib-rearing. The preadaptation hypothesis has recently received empirical support, but remains to be formalised. Here, we mathematically model the coevolution of sex-specific helping and sex allocation, contrasting these hypotheses. We find that ploidy per se has little effect. Rather, the ecology of sex shapes patterns of helping: sex-specific preadaptation strongly influences who helps; a freely adjustable sex ratio magnifies sex biases and promotes helping; and sib-mating, promiscuity, and reproductive autonomy also modulate the sex and abundance of helpers. An empirical survey reveals that patterns of sex-specific helping in arthropod taxa are consistent with the preadaptation hypothesis.Publisher PDFPeer reviewe
Transverse polarization in inclusive quasi-real photoproduction at the current fragmentation
It is shown that the recent HERMES data on the transverse
polarization in the inclusive quasi-real photoproduction at can be
accommodated by the strange quark scattering model. Relations with the quark
recombination approach are discussed.Comment: 5 pages, 3 figures, accepted by Eur. Phys. J.
- âŠ