3,467 research outputs found
Gravitational Collapse of Dust with a Cosmological Constant
The recent analysis of Markovic and Shapiro on the effect of a cosmological
constant on the evolution of a spherically symmetric homogeneous dust ball is
extended to include the inhomogeneous and degenerate cases. The histories are
shown by way of effective potential and Penrose-Carter diagrams.Comment: 2 pages, 2 figures (png), revtex. To appear in Phys. Rev.
Oscillating Fracture in Rubber
We have found an oscillating instability of fast-running cracks in thin
rubber sheets. A well-defined transition from straight to oscillating cracks
occurs as the amount of biaxial strain increases. Measurements of the amplitude
and wavelength of the oscillation near the onset of this instability indicate
that the instability is a Hopf bifurcation
Adventures in Invariant Theory
We provide an introduction to enumerating and constructing invariants of
group representations via character methods. The problem is contextualised via
two case studies arising from our recent work: entanglement measures, for
characterising the structure of state spaces for composite quantum systems; and
Markov invariants, a robust alternative to parameter-estimation intensive
methods of statistical inference in molecular phylogenetics.Comment: 12 pp, includes supplementary discussion of example
Static Ricci-flat 5-manifolds admitting the 2-sphere
We examine, in a purely geometrical way, static Ricci-flat 5-manifolds
admitting the 2-sphere and an additional hypersurface-orthogonal Killing
vector. These are widely studied in the literature, from different physical
approaches, and known variously as the Kramer - Gross - Perry - Davidson - Owen
solutions. The 2-fold infinity of cases that result are studied by way of new
coordinates (which are in most cases global) and the cases likely to be of
interest in any physical approach are distinguished on the basis of the
nakedness and geometrical mass of their associated singularities. It is argued
that the entire class of solutions has to be considered unstable about the
exceptional solutions: the black string and soliton cases. Any physical theory
which admits the non-exceptional solutions as the external vacuua of a
collapsing object has to accept the possibility of collapse to zero volume
leaving behind the weakest possible, albeit naked, geometrical singularities at
the origin.Finally, it is pointed out that these types of solutions generalize,
in a straightforward way, to higher dimensions.Comment: Generalize, in a straightforward way, to higher dimension
Duality extended Chaplygin cosmologies with a big rip
We consider modifications to the Friedmann equation motivated by recent
proposals along these lines pursuing an explanation to the observed late time
acceleration. Here we show those modifications can be framed within a theory
with self-interacting gravity, where the term self-interaction refers here to
the presence of functions of and in the right hand side of the
Einstein equations. We then discuss the construction of the duals of the
cosmologies generated within that framework. After that we investigate the
modifications required to generate generalized and modified Chaplygin
cosmologies and show that their duals belong to a larger family of cosmologies
we call extended Chaplygin cosmologies. Finally, by letting the parameters of
those models take values not earlier considered in the literature we show some
representatives of that family of cosmologies display sudden future
singularities, which indicates their behavior is rather different from
generalized or modified Chaplygin gas cosmologies. This reinforces the idea
that modifications of gravity can be responsible for unexpected evolutionary
features in the universe.Comment: 5 pages, revtex
Junctions and thin shells in general relativity using computer algebra I: The Darmois-Israel Formalism
We present the GRjunction package which allows boundary surfaces and
thin-shells in general relativity to be studied with a computer algebra system.
Implementing the Darmois-Israel thin shell formalism requires a careful
selection of definitions and algorithms to ensure that results are generated in
a straight-forward way. We have used the package to correctly reproduce a wide
variety of examples from the literature. We present several of these
verifications as a means of demonstrating the packages capabilities. We then
use GRjunction to perform a new calculation - joining two Kerr solutions with
differing masses and angular momenta along a thin shell in the slow rotation
limit.Comment: Minor LaTeX error corrected. GRjunction for GRTensorII is available
from http://astro.queensu.ca/~grtensor/GRjunction.htm
Six Peaks Visible in the Redshift Distribution of 46,400 SDSS Quasars Agree with the Preferred Redshifts Predicted by the Decreasing Intrinsic Redshift Model
The redshift distribution of all 46,400 quasars in the Sloan Digital Sky
Survey (SDSS) Quasar Catalog III, Third Data Release, is examined. Six Peaks
that fall within the redshift window below z = 4, are visible. Their positions
agree with the preferred redshift values predicted by the decreasing intrinsic
redshift (DIR) model, even though this model was derived using completely
independent evidence. A power spectrum analysis of the full dataset confirms
the presence of a single, significant power peak at the expected redshift
period. Power peaks with the predicted period are also obtained when the upper
and lower halves of the redshift distribution are examined separately. The
periodicity detected is in linear z, as opposed to log(1+z). Because the peaks
in the SDSS quasar redshift distribution agree well with the preferred
redshifts predicted by the intrinsic redshift relation, we conclude that this
relation, and the peaks in the redshift distribution, likely both have the same
origin, and this may be intrinsic redshifts, or a common selection effect.
However, because of the way the intrinsic redshift relation was determined it
seems unlikely that one selection effect could have been responsible for both.Comment: 12 pages, 12 figure, accepted for publication in the Astrophysical
Journa
A Novel Longitudinal Mode in the Coupled Quantum Chain Compound KCuF3
Inelastic neutron scattering measurements are reported that show a new
longitudinal mode in the antiferromagnetically ordered phase of the spin-1/2
quasi-one-dimensional antiferromagnet KCuF3. This mode signals the cross-over
from one-dimensional to three-dimensional behavior and indicates a reduction in
the ordered spin moment of a spin-1/2 antiferromagnet. The measurements are
compared with recent quantum field theory results and are found to be in
excellent agreement. A feature of the data not predicted by theory is a damping
of the mode by decay processes to the transverse spin-wave branches.Comment: 9 pages of text plus 4 postscript figures (1 color
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