Shear-Free Gravitational Waves in an Anisotropic Universe

We study gravitational waves propagating through an anisotropic Bianchi I dust-filled universe (containing the Einstein-de-Sitter universe as a special case). The waves are modeled as small perturbations of this background cosmological model and we choose a family of null hypersurfaces in this space-time to act as the histories of the wavefronts of the radiation. We find that the perturbations we generate can describe pure gravitational radiation if and only if the null hypersurfaces are shear-free. We calculate the gauge-invariant small perturbations explicitly in this case. How these differ from the corresponding perturbations when the background space-time is isotropic is clearly exhibited.Comment: 32 pages, accepted for publication in Physical Review

Light-like Signals in General relativity and Cosmology

The modelling of light-like signals in General Relativity taking the form of impulsive gravitational waves and light-like shells of matter is examined. Systematic deductions from the Bianchi identities are made. These are based upon Penrose's hierarchical classification of the geometry induced on the null hypersurface history of the surface by its imbedding in the space-times to the future and to the past of it. The signals are not confined to propagate in a vacuum and thus their interaction with matter (a burst of radiation propagating through a cosmic fluid, for example) is also studied. Results are accompanied by illustrative examples using cosmological models, vacuum space-times, the de sitter univers and Minkowskian space-time.Comment: 21 pages, latex, no figure

Peeling properties of lightlike signals in General Relativity

The peeling properties of a lightlike signal propagating through a general Bondi-Sachs vacuum spacetime and leaving behind another Bondi-Sachs vacuum space-time are studied. We demonstrate that in general the peeling behavior is the conventional one which is associated with a radiating isolated system and that it becomes unconventional if the asymptotically flat space-times on either side of the history of the light-like signal tend to flatness at future null infinity faster than the general Bondi-Sachs space-time. This latter situation occurs if, for example, the space-times in question are static Bondi-Sachs space- times.Comment: 14 pages, LaTeX2

Gravitational Wave Propagation in Isotropic Cosmologies

We study the propagation of gravitational waves carrying arbitrary information through isotropic cosmologies. The waves are modelled as small perturbations of the background Robertson-Walker geometry. The perfect fluid matter distribution of the isotropic background is, in general, modified by small anisotropic stresses. For pure gravity waves, in which the perturbed Weyl tensor is radiative (i.e. type N in the Petrov classification), we construct explicit examples for which the presence of the anisotropic stress is shown to be essential and the histories of the wave-fronts in the background Robertson-Walker geometry are shear-free null hypersurfaces. The examples derived in this case are analogous to the Bateman waves of electromagnetic theory.Comment: 27 pages, accepted for publication in Phys.Rev.

On Generating Gravity Waves with Matter and Electromagnetic Waves

If a homogeneous plane light-like shell collides head-on with a homogeneous plane electromagnetic shock wave having a step-function profile then no backscattered gravitational waves are produced. We demonstrate, by explicit calculation, that if the matter is accompanied by a homogeneous plane electromagnetic shock wave with a step-function profile then backscattered gravitational waves appear after the collision.Comment: Latex file, 15 pages, accepted for publication in Physical Review

Multi-layer graphene as a selective detector for future lung cancer biosensing platforms

This is the final version. Available from the Royal Society of Chemistry via the DOI in this record.Highly selective, fast detection of specific lung-cancer biomarkers (CMs) in exhaled human breath is vital to the development of enhanced sensing devices. Today, e-nose is a promising approach for the diagnosis of lung cancer. Nevertheless, considerable challenges to early-stage disease diagnostics still remain: e.g. decrease in sensor sensitivities in the presence of water vapor, sensor drift leading to the inability to calibrate exactly, relatively short sensor lifetimes, and difficulty discriminating between multiple diseases. However, there is a wide scope for breath diagnostics techniques, and all advanced electrodes applicable to e-nose devices will benefit them. Here, we present the promising sensing capabilities of bare multi-layer graphene (MLG) as a proof of concept for advanced e-nose devices and demonstrate its utility for biomolecule discrimination of the most common lung CMs (ethanol, isopropanol, and acetone). We report on a comparative study involving exposure of the three CM solutions on flat MLG (f-MLG) and patterned MLG (p-MLG) electrodes, where the electrical conductivity of p-MLG is significantly increased while applying acetone. Based on sensitivity tests, we demonstrate the ability to monitor the electrical response of graphene electrodes employing graphene of various wettabilities. Specifically, the f-MLG electrode displays almost 2 times higher sheet resistance (30 Ω sq−1) compared to the hydrophilic p-MLG (12 Ω sq−1). We show significant sensitivity to selected specific molecules of pristine f-MLG and p-MLG while applying CM solutions with a 1.4 × 105 ppm concentration. Finally, we show the selectivity of f-MLG and p-MLG-based sensors when exposed to 2.0 × 105 ppm solutions containing different CM combinations. Both sensors were selective in particular to acetone, since the presence of acetone leads to a sheet resistance increase. We demonstrate that an advanced e-nose approach integrated with MLG electrodes has significant potential as a design concept for utilization of molecular detection at variable concentrations such as in early-stage disease diagnosis. This early-stage approach will provide convenient and reusable complex monitoring of CMs compared to typical contact sensors which require target analysis and are limited by disposable measuring. Moreover, further integration of the Internet of Things will introduce advanced e-nose devices as a biotechnological innovation for disease resilience with the potential for commercialization.Engineering and Physical Sciences Research Council (EPSRC)Engineering and Physical Sciences Research Council (EPSRC

The Bell-Szekeres Solution and Related Solutions of the Einstein-Maxwell Equations

A novel technique for solving some head-on collisions of plane homogeneous light-like signals in Einstein-Maxwell theory is described. The technique is a by-product of a re-examination of the fundamental Bell-Szekeres solution in this field of study. Extensions of the Bell-Szekeres collision problem to include light-like shells and gravitational waves are described and a family of solutions having geometrical and topological properties in common with the Bell-Szekeres solution is derived.Comment: 18 pages, Latex fil

Some Physical Consequences of Abrupt Changes in the Multipole Moments of a Gravitating Body

The Barrab\`es-Israel theory of light-like shells in General Relativity is used to show explicitly that in general a light-like shell is accompanied by an impulsive gravitational wave. The gravitational wave is identified by its Petrov Type N contribution to a Dirac delta-function term in the Weyl conformal curvature tensor (with the delta-function singular on the null hypersurface history of the wave and shell). An example is described in which an asymptotically flat static vacuum Weyl space-time experiences a sudden change across a null hypersurface in the multipole moments of its isolated axially symmetric source. A light-like shell and an impulsive gravitational wave are identified, both having the null hypersurface as history. The stress-energy in the shell is dominated (at large distance from the source) by the jump in the monopole moment (the mass) of the source with the jump in the quadrupole moment mainly responsible for the stress being anisotropic. The gravitational wave owes its existence principally to the jump in the quadrupole moment of the source confirming what would be expected.Comment: 26 pages, tex, no figures, to appear in Phys.Rev.

Seeking the Ultraviolet Ionizing Background at z~3 with the Keck Telescope

We describe the initial results of a deep long-slit emission line search for redshifted (2.7<z<4.1) Lyman-alpha. These observations are used to constrain the fluorescent Ly-alpha emission from the population of clouds whose absorption produces the higher-column-density component of the Ly-alpha forest in quasar spectra. We use the results to set an upper limit on the ultraviolet ionizing background. Our spectroscopic data obtained with the Keck II telescope at lambda/(Delta lambda FWHM)~2000 reveals no candidate Ly-alpha emission over the wavelength range of 4500-6200 Ang along a 3 arcmin slit in a 5400 s integration. Our 3 sigma upper bound on the mean intensity of the ionizing background at the Lyman limit is J(nu 0) < 2E-21 erg/s/cm**2/Hz/sr for 2.7<z<3.1 (where we are most sensitive), assuming Lyman limit systems have typical radii of 70 kpc (q_0=0.5, H_0=50 km/s/Mpc). This constraint is more than an order of magnitude more stringent than any previously published direct limit. However, it is still a factor of three above the ultraviolet background level expected due to the integrated light of known quasars at z~3. This pilot study confirms the conclusion of Gould \& Weinberg (1996) that integrations of several hours on a 10-m class telescope should be capable of measuring J(nu 0) at high redshift.Comment: 22 pages, 2 postscipt figures. Latex requires aaspp4.sty and epsf.sty (included). Accepted for publication in the Astronomical Journal (Nov 1998

Large-amplitude isothermal fluctuations and high-density dark-matter clumps

Large-amplitude isothermal fluctuations in the dark matter energy density, parameterized by \Phi\equiv\delta\rhodm/\rhodm, are studied within the framework of a spherical collapse model. For \Phi \ga 1, a fluctuation collapses in the radiation-dominated epoch and produces a dense dark-matter object. The final density of the virialized object is found to be \rho_F \approx 140\, \Phi^3 (\Phi+1) \rhoeq, where \rhoeq is the matter density at equal matter and radiation energy density. This expression is valid for the entire range of possible values of $\Phi$, both for $\Phi \gg 1$ and $\Phi \ll 1$. Some astrophysical consequences of high-density dark-matter clumps are discussed.Comment: 15 pages plus 3 figures (included at the end as a uuencoded postscript file), LaTeX, FNAL--PUB--94/055--