Stability of Gravitational and Electromagnetic Geons

Recent work on gravitational geons is extended to examine the stability properties of gravitational and electromagnetic geon constructs. All types of geons must possess the property of regularity, self-consistency and quasi-stability on a time-scale much longer than the period of the comprising waves. Standard perturbation theory, modified to accommodate time-averaged fields, is used to test the requirement of quasi-stability. It is found that the modified perturbation theory results in an internal inconsistency. The time-scale of evolution is found to be of the same order in magnitude as the period of the comprising waves. This contradicts the requirement of slow evolution. Thus not all of the requirements for the existence of electromagnetic or gravitational geons are met though perturbation theory. From this result it cannot be concluded that an electromagnetic or a gravitational geon is a viable entity. The broader implications of the result are discussed with particular reference to the problem of gravitational energy.Comment: 40 pages, 5 EPS figures, uses overcite.st

The need for dark matter in galaxies

Cooperstock and Tieu have proposed a model to account for galactic rotation curves without invoking dark matter. I argue that no model of this type can work

Energy and Momentum of a Class of Rotating Gravitational Waves

We calculate energy and momentum for a class of cylindrical rotating gravitational waves using Einstein and Papapetrou's prescriptions. It is shown that the results obtained are reduced to the special case of the cylindrical gravitational waves already available in the literature.Comment: 11 pages, no figure, Late

Negative Pressure and Naked Singularities in Spherical Gravitational Collapse

Assuming the weak energy condition, we study the nature of the non-central shell-focussing singularity which can form in the gravitational collapse of a spherical compact object in classical general relativity. We show that if the radial pressure is positive, the singularity is covered by a horizon. For negative radial pressures, the singularity will be covered if the ratio of pressure to the density is greater than -1/3 and naked if this ratio is $\leq -1/3$.Comment: 7 pages, LaTeX Fil

Energy and Momentum densities of cosmological models, with equation of state ρ=μ\rho=\mu, in general relativity and teleparallel gravity

We calculated the energy and momentum densities of stiff fluid solutions, using Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum complexes, in both general relativity and teleparallel gravity. In our analysis we get different results comparing the aforementioned complexes with each other when calculated in the same gravitational theory, either this is in general relativity and teleparallel gravity. However, interestingly enough, each complex's value is the same either in general relativity or teleparallel gravity. Our results sustain that (i) general relativity or teleparallel gravity are equivalent theories (ii) different energy-momentum complexes do not provide the same energy and momentum densities neither in general relativity nor in teleparallel gravity. In the context of the theory of teleparallel gravity, the vector and axial-vector parts of the torsion are obtained. We show that the axial-vector torsion vanishes for the space-time under study.Comment: 15 pages, no figures, Minor typos corrected; version to appear in International Journal of Theoretical Physic

The response of laser interferometers to a gravitational wave

Laser interferometer detectors are now widely used in an attempt to detect gravitational waves (gw). The interaction of the gw with the light circulating in the interferometer is usually explained in terms of the motion of the "free" mirrors that form the interferometer arms. It is however instructive to show that the same result can be obtained by simply calculating the propagation of an electromagnetic plane wave between "free mirrors" in the curved space-time induced by the gw. One finds that the plane wave acquires frequency modulation sidebands at the gw frequency, as would be expected from the absorption and emission of gravitons from and to the gw. Such sidebands are completely equivalent to the time-dependent phase shift imposed on the plane wave, that follows from the conventional calculation

Gene Catchr—Gene Cloning And Tagging for Caenorhabditis elegans using yeast Homologous Recombination: a novel approach for the analysis of gene expression

Expression patterns of gene products provide important insights into gene function. Reporter constructs are frequently used to analyze gene expression in Caenorhabditis elegans, but the sequence context of a given gene is inevitably altered in such constructs. As a result, these transgenes may lack regulatory elements required for proper gene expression. We developed Gene Catchr, a novel method of generating reporter constructs that exploits yeast homologous recombination (YHR) to subclone and tag worm genes while preserving their local sequence context. YHR facilitates the cloning of large genomic regions, allowing the isolation of regulatory sequences in promoters, introns, untranslated regions and flanking DNA. The endogenous regulatory context of a given gene is thus preserved, producing expression patterns that are as accurate as possible. Gene Catchr is flexible: any tag can be inserted at any position without introducing extra sequence. Each step is simple and can be adapted to process multiple genes in parallel. We show that expression patterns derived from Gene Catchr transgenes are consistent with previous reports and also describe novel expression data. Mutant rescue assays demonstrate that Gene Catchr-generated transgenes are functional. Our results validate the use of Gene Catchr as a valuable tool to study spatiotemporal gene expression

Energy and Momentum Distributions of Kantowski and Sachs Space-time

We use the Einstein, Bergmann-Thomson, Landau-Lifshitz and Papapetrou energy-momentum complexes to calculate the energy and momentum distributions of Kantowski and Sachs space-time. We show that the Einstein and Bergmann-Thomson definitions furnish a consistent result for the energy distribution, but the definition of Landau-Lifshitz do not agree with them. We show that a signature switch should affect about everything including energy distribution in the case of Einstein and Papapetrou prescriptions but not in Bergmann-Thomson and Landau-Lifshitz prescriptions.Comment: 12 page

The gravitational interaction of light: from weak to strong fields

An explanation is proposed for the fact that pp-waves superpose linearly when they propagate parallely, while they interact nonlinearly, scatter and form singularities or Cauchy horizons if they are antiparallel. Parallel pp-waves do interact, but a generalized gravitoelectric force is exactly cancelled by a gravitomagnetic force. In an analogy, the interaction of light beams in linearized general relativity is also revisited and clarified, a new result is obtained for photon to photon attraction, and a conjecture is proved. Given equal energy density in the beams, the light-to-light attraction is twice the matter-to-light attraction and four times the matter-to-matter attraction.Comment: 17 pages, LaTeX, no figures. To appear in General Relativity and Gravitatio

The abstract boundary---a new approach to singularities of manifolds

A new scheme is proposed for dealing with the problem of singularities in General Relativity. The proposal is, however, much more general than this. It can be used to deal with manifolds of any dimension which are endowed with nothing more than an affine connection, and requires a family \calc\ of curves satisfying a {\em bounded parameter property} to be specified at the outset. All affinely parametrised geodesics are usually included in this family, but different choices of family \calc\ will in general lead to different singularity structures. Our key notion is the {\em abstract boundary\/} or {\em $a$-boundary\/} of a manifold, which is defined for any manifold \calm\ and is independent of both the affine connection and the chosen family \calc\ of curves. The $a$-boundary is made up of equivalence classes of boundary points of \calm\ in all possible open embeddings. It is shown that for a pseudo-Riemannian manifold (\calm,g) with a specified family \calc\ of curves, the abstract boundary points can then be split up into four main categories---regular, points at infinity, unapproachable points and singularities. Precise definitions are also provided for the notions of a {\em removable singularity} and a {\em directional singularity}. The pseudo-Riemannian manifold will be said to be singularity-free if its abstract boundary contains no singularities. The scheme passes a number of tests required of any theory of singularities. For instance, it is shown that all compact manifolds are singularity-free, irrespective of the metric and chosen family \calc.Comment: 40 pages (amslatex) + 5 uuencoded figures (A postscript version is also available on http://einstein.anu.edu.au/), CMA Maths. Research Report No. MRR028-9