222 research outputs found
All conformally flat pure radiation metrics
The complete class of conformally flat, pure radiation metrics is given,
generalising the metric recently given by Wils.Comment: 7 pages, plain Te
Goitre and Iodine Deficiency in Europe
The prevalence of endemic iodine-deficiency goitre in Europe has been reduced in many areas by the introduction of iodination programmes. Recent reports, however, show that goitre remains a significant problem and that its prevalence has not decreased in a number of European countries. Hetzel1 has pointed out that the high global prevalence of iodine-deficiency disorders could be eradicated within 5-10 years by introduction of an iodised salt programme. The current World Health Organisation recommendations for iodine intake are between 150 and 300 μg/da
Axial symmetry and conformal Killing vectors
Axisymmetric spacetimes with a conformal symmetry are studied and it is shown
that, if there is no further conformal symmetry, the axial Killing vector and
the conformal Killing vector must commute. As a direct consequence, in
conformally stationary and axisymmetric spacetimes, no restriction is made by
assuming that the axial symmetry and the conformal timelike symmetry commute.
Furthermore, we prove that in axisymmetric spacetimes with another symmetry
(such as stationary and axisymmetric or cylindrically symmetric spacetimes) and
a conformal symmetry, the commutator of the axial Killing vector with the two
others mush vanish or else the symmetry is larger than that originally
considered. The results are completely general and do not depend on Einstein's
equations or any particular matter content.Comment: 15 pages, Latex, no figure
Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics, with zero cosmological constant
Metrics obtained by integrating within the generalised invariant formalism
are structured around their intrinsic coordinates, and this considerably
simplifies their invariant classification and symmetry analysis. We illustrate
this by presenting a simple and transparent complete invariant classification
of the conformally flat pure radiation metrics (except plane waves) in such
intrinsic coordinates; in particular we confirm that the three apparently
non-redundant functions of one variable are genuinely non-redundant, and easily
identify the subclasses which admit a Killing and/or a homothetic Killing
vector. Most of our results agree with the earlier classification carried out
by Skea in the different Koutras-McIntosh coordinates, which required much more
involved calculations; but there are some subtle differences. Therefore, we
also rework the classification in the Koutras-McIntosh coordinates, and by
paying attention to some of the subtleties involving arbitrary functions, we
are able to obtain complete agreement with the results obtained in intrinsic
coordinates. In particular, we have corrected and completed statements and
results by Edgar and Vickers, and by Skea, about the orders of Cartan
invariants at which particular information becomes available.Comment: Extended version of GRG publication, with some typos etc correcte
On limits of spacetimes -- a coordinate-free approach
A coordinate-free approach to limits of spacetimes is developed. The limits
of the Schwarzschild metric as the mass parameter tends to 0 or are
studied, extending previous results. Besides the known Petrov type D and 0
limits, three vacuum plane-wave solutions of Petrov type N are found to be
limits of the Schwarzschild spacetime.Comment: 19 p
On the Symmetries of the Edgar-Ludwig Metric
The conformal Killing equations for the most general (non-plane wave)
conformally flat pure radiation field are solved to find the conformal Killing
vectors. As expected fifteen independent conformal Killing vectors exist, but
in general the metric admits no Killing or homothetic vectors. However for
certain special cases a one-dimensional group of homotheties or motions may
exist and in one very special case, overlooked by previous investigators, a
two-dimensional homethety group exists. No higher dimensional groups of motions
or homotheties are admitted by these metrics.Comment: Plain TeX, 7 pages, No figure
Interpreting a conformally flat pure radiation space-time
A physical interpretation is presented of the general class of conformally
flat pure radiation metrics that has recently been identified by Edgar and
Ludwig. It is shown that, at least in the weak field limit, successive wave
surfaces can be represented as null (half) hyperplanes rolled around a
two-dimensional null cone. In the impulsive limit, the solution reduces to a
pp-wave whose direction of propagation depends on retarded time. In the general
case, there is a coordinate singularity which corresponds to an envelope of the
wave surfaces. The global structure is discussed and a possible vacuum
extension through the envelope is proposed.Comment: 9 pages, Plain TeX, 2 figures. To appear in Class. Quantum Grav.
Reference adde
Self-similar Bianchi type VIII and IX models
It is shown that in transitively self-similar spatially homogeneous tilted
perfect fluid models the symmetry vector is not normal to the surfaces of
spatial homogeneity. A direct consequence of this result is that there are no
self-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore the
most general Bianchi VIII and IX spacetime which admit a four dimensional group
of homotheties is given.Comment: 5 pages, Latex; One reference and minor clarifications added. To
appear in General Relativity and Gravitatio
On the limits of Brans-Dicke spacetimes: a coordinate-free approach
We investigate the limit of Brans-Dicke spacetimes as the scalar field
coupling constant omega tends to infinity applying a coordinate-free technique.
We obtain the limits of some known exact solutions. It is shown that these
limits may not correspond to similar solutions in the general relativity
theory.Comment: LaTeX, 16 pp, report DF/UFPB/02-9
Obtaining a class of Type O pure radiation metrics with a cosmological constant, using invariant operators
Using the generalised invariant formalism we derive a class of conformally
flat spacetimes whose Ricci tensor has a pure radiation and a Ricci scalar
component. The method used is a development of the methods used earlier for
pure radiation spacetimes of Petrov types O and N respectively. In this paper
we demonstrate how to handle, in the generalised invariant formalism,
spacetimes with isotropy freedom and rich Killing vector structure. Once the
spacetimes have been constructed, it is straightforward to deduce their
Karlhede classification: the Karlhede algorithm terminates at the fourth
derivative order, and the spacetimes all have one degree of null isotropy and
three, four or five Killing vectors.Comment: 29 page
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