765 research outputs found
Lie symmetries for equations in conformal geometries
We seek exact solutions to the Einstein field equations which arise when two
spacetime geometries are conformally related. Whilst this is a simple method to
generate new solutions to the field equations, very few such examples have been
found in practice. We use the method of Lie analysis of differential equations
to obtain new group invariant solutions to conformally related Petrov type D
spacetimes. Four cases arise depending on the nature of the Lie symmetry
generator. In three cases we are in a position to solve the master field
equation in terms of elementary functions. In the fourth case special solutions
in terms of Bessel functions are obtained. These solutions contain known models
as special cases.Comment: 19 pages, To appear in J. Phys.
Nonperturbative gravito-magnetic fields
In a cold matter universe, the linearized gravito-magnetic tensor field
satisfies a transverse condition (vanishing divergence) when it is purely
radiative. We show that in the nonlinear theory, it is no longer possible to
maintain the transverse condition, since it leads to a non-terminating chain of
integrability conditions. These conditions are highly restrictive, and are
likely to hold only in models with special symmetries, such as the known
Bianchi and examples. In models with realistic inhomogeneity, the
gravito-magnetic field is necessarily non-transverse at second and higher
order.Comment: Minor changes to match published version; to appear in Phys. Rev.
Anisotropic stresses in inhomogeneous universes
Anisotropic stress contributions to the gravitational field can arise from
magnetic fields, collisionless relativistic particles, hydrodynamic shear
viscosity, gravitational waves, skew axion fields in low-energy string
cosmologies, or topological defects. We investigate the effects of such
stresses on cosmological evolution, and in particular on the dissipation of
shear anisotropy. We generalize some previous results that were given for
homogeneous anisotropic universes, by including small inhomogeneity in the
universe. This generalization is facilitated by a covariant approach. We find
that anisotropic stress dominates the evolution of shear, slowing its decay.
The effect is strongest in radiation-dominated universes, where there is slow
logarithmic decay of shear.Comment: 7 pages Revte
Obtaining the spacetime metric from cosmological observations
Recent galaxy redshift surveys have brought in a large amount of accurate
cosmological data out to redshift 0.3, and future surveys are expected to
achieve a high degree of completeness out to a redshift exceeding 1.
Consequently, a numerical programme for determining the metric of the universe
from observational data will soon become practical; and thereby realise the
ultimate application of Einstein's equations. Apart from detailing the cosmic
geometry, this would allow us to verify and quantify homogeneity, rather than
assuming it, as has been necessary up to now, and to do that on a metric level,
and not merely at the mass distribution level. This paper is the beginning of a
project aimed at such a numerical implementation. The primary observational
data from our past light cone consists of galaxy redshifts, apparent
luminosities, angular diameters and number densities, together with source
evolution functions, absolute luminosities, true diameters and masses of
sources. Here we start with the simplest case, that of spherical symmetry and a
dust equation of state, and execute an algorithm that determines the unknown
metric functions from this data. We discuss the challenges of turning the
theoretical algorithm into a workable numerical procedure, particularly
addressing the origin and the maximum in the area distance. Our numerical
method is tested with several artificial data sets for homogeneous and
inhomogeneous models, successfully reproducing the original models. This
demonstrates the basic viability of such a scheme. Although current surveys
don't have sufficient completeness or accuracy, we expect this situation to
change in the near future, and in the meantime there are many refinements and
generalisations to be added.Comment: 26 pages, 10 figures. Minor changes to match the published versio
A classification of spherically symmetric spacetimes
A complete classification of locally spherically symmetric four-dimensional
Lorentzian spacetimes is given in terms of their local conformal symmetries.
The general solution is given in terms of canonical metric types and the
associated conformal Lie algebras. The analysis is based upon the local
conformal decomposition into 2+2 reducible spacetimes and the Petrov type. A
variety of physically meaningful example spacetimes are discussed
Matching of spatially homogeneous non-stationary space--times to vacuum in cylindrical symmetry
We study the matching of LRS spatially homogeneous collapsing dust
space-times with non-stationary vacuum exteriors in cylindrical symmetry. Given
an interior with diagonal metric we prove existence and uniqueness results for
the exterior. The matched solutions contain trapped surfaces, singularities and
Cauchy horizons. The solutions cannot be asymptotically flat and we present
evidence that they are singular on the Cauchy horizons.Comment: LaTeX, 15 pages, 1 figure, submitted for publicatio
Local freedom in the gravitational field revisited
Maartens {\it et al.}\@ gave a covariant characterization, in a 1+3 formalism
based on a perfect fluid's velocity, of the parts of the first derivatives of
the curvature tensor in general relativity which are ``locally free'', i.e. not
pointwise determined by the fluid energy momentum and its derivative. The full
decomposition of independent curvature derivative components given in earlier
work on the spinor approach to the equivalence problem enables analogous
general results to be stated for any order: the independent matter terms can
also be characterized. Explicit relations between the two sets of results are
obtained. The 24 Maartens {\it et al.} locally free data are shown to
correspond to the quantities in the spinor approach, and the
fluid terms are similarly related to the remaining 16 independent quantities in
the first derivatives of the curvature.Comment: LaTeX. 13 pp. To be submitted to Class. Quant. Gra
Brane-World Black Hole Solutions via a Confining Potential
Using a confining potential, we consider spherically symmetric vacuum (static
black hole) solutions in a brane-world scenario. Working with a constant
curvature bulk, two interesting cases/solutions are studied. A Schwarzschild-de
Sitter black hole solution similar to the standard solution in the presence of
a cosmological constant is obtained which confirms the idea that an extra term
in the field equations on the brane can play the role of a positive
cosmological constant and may be used to account for the accelerated expansion
of the universe. The other solution is one in which we can have a proper
potential to explain the galaxy rotation curves without assuming the existence
of dark matter and without working with new modified theories (modified
Newtonian dynamics).Comment: 12 pages, to appear in PR
Density perturbations in the brane-world
In Randall-Sundrum-type brane-world cosmologies, density perturbations
generate Weyl curvature in the bulk, which in turn backreacts on the brane via
stress-energy perturbations. On large scales, the perturbation equations
contain a closed system on the brane, which may be solved without solving for
the bulk perturbations. Bulk effects produce a non-adiabatic mode, even when
the matter perturbations are adiabatic, and alter the background dynamics. As a
consequence, the standard evolution of large-scale fluctuations in general
relativity is modified. The metric perturbation on large-scales is not constant
during high-energy inflation. It is constant during the radiation era, except
at most during the very beginning, if the energy is high enough.Comment: Additional arguments and minor corrections; version accepted by Phys.
Rev.
Genetic variability in barley (Hordeum vulgare L.) landraces from Ethiopia as measured by morphological characters and SDS-page of seed storage proteins
Data on 44 barley landraces comprising collections and farmers’ cultivars from north Shewa, Ethiopia were studied for variability in morphological characters and Sodium Dodecyl Sulphate Polyacrylamide Gel Electophoresis (SDS-PAGE) of seed storage proteins. The phenotypic frequencies of morphological characters (qualitative and quantitative) were analysed by the Shanon Weaver diversity index (H’) to estimate within landrace genetic variability for individual characters. Variability for seed protein banding patterns was assessed by SDS-PAGE. Both morphological and SDS-PAGE data demonstrated the variability existing in the landraces. H’ values pooled over morphological characters ranged from 0.12 to 0.58. Among the qualitative characters, landraces showed higher levels of polymorphism for spike type than for kernel color, spike density and caryopsis type (covered or naked). Caryopsis type was the least diverse character observed. Diversity for quantitative characters pooled over landraces was generally very high especially for number of seeds spike-1 and days to maturity with respective H’ values of 0.90 and 0.98. DS-PAGE data based on representative lines from each landrace showed very low to high within landrace variability for banding patterns. Lines from landraces differed from each other in number and migration distances of bands. Some landraces that looked uniform for spike morphology also showed differences in banding patterns. It was also observed, on the other hand, that some landraces displaying different spike characters and hence assumed to exhibit differences of comparable magnitude in storage protein variability did not reveal much differences. Variability between landraces was higher than within landraces and variability within farmers’ cultivars was lower than within accessions. Clustering results of landraces from SDS-PAGE data were different in composition from those formed by morphological characters. Clustering from morphological data highlighted distinct grouping of landraces based on similarities in morphological characters whereas SDS-PAGE data did not depict such distinctness
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