Massive fields tend to form highly oscillating self-similarly expanding shells

The time evolution of self-interacting spherically symmetric scalar fields in Minkowski spacetime is investigated based on the use of Green's theorem. It is shown that a massive Klein-Gordon field can be characterized by the formation of certain expanding shell structures where all the shells are built up by very high frequency oscillations. This oscillation is found to be modulated by the product of a simple time decaying factor of the form $t^{-{3}/{2}}$ and of an essentially self-similar expansion. Apart from this self-similar expansion the developed shell structure is preserved by the evolution. In particular, the energy transported by each shell appears to be time independent.Comment: 10 pages, to appear in Phys. Rev.

Numerical simulation of the massive scalar field evolution in the Reissner-Nordstr\"{o}m black hole background

We studied the massive scalar wave propagation in the background of Reissner-Nordstr\"{o}m black hole by using numerical simulations. We learned that the value $Mm$ plays an important role in determining the properties of the relaxation of the perturbation. For $Mm << 1$ the relaxation process depends only on the field parameter and does not depend on the spacetime parameters. For $Mm >> 1$, the dependence of the relaxation on the black hole parameters appears. The bigger mass of the black hole, the faster the perturbation decays. The difference of the relaxation process caused by the black hole charge $Q$ has also been exhibited.Comment: Accepted for publication in Phys. Rev.

Radiative falloff of a scalar field in a weakly curved spacetime without symmetries

We consider a massless scalar field propagating in a weakly curved spacetime whose metric is a solution to the linearized Einstein field equations. The spacetime is assumed to be stationary and asymptotically flat, but no other symmetries are imposed -- the spacetime can rotate and deviate strongly from spherical symmetry. We prove that the late-time behavior of the scalar field is identical to what it would be in a spherically-symmetric spacetime: it decays in time according to an inverse power-law, with a power determined by the angular profile of the initial wave packet (Price falloff theorem). The field's late-time dynamics is insensitive to the nonspherical aspects of the metric, and it is governed entirely by the spacetime's total gravitational mass; other multipole moments, and in particular the spacetime's total angular momentum, do not enter in the description of the field's late-time behavior. This extended formulation of Price's falloff theorem appears to be at odds with previous studies of radiative decay in the spacetime of a Kerr black hole. We show, however, that the contradiction is only apparent, and that it is largely an artifact of the Boyer-Lindquist coordinates adopted in these studies.Comment: 17 pages, RevTeX

Computing gravitational waves from slightly nonspherical stellar collapse to black hole: Odd-parity perturbation

Nonspherical stellar collapse to a black hole is one of the most promising gravitational wave sources for gravitational wave detectors. We numerically study gravitational waves from a slightly nonspherical stellar collapse to a black hole in linearized Einstein theory. We adopt a spherically collapsing star as the zeroth-order solution and gravitational waves are computed using perturbation theory on the spherical background. In this paper we focus on the perturbation of odd-parity modes. Using the polytropic equations of state with polytropic indices $n_p=1$ and 3, we qualitatively study gravitational waves emitted during the collapse of neutron stars and supermassive stars to black holes from a marginally stable equilibrium configuration. Since the matter perturbation profiles can be chosen arbitrarily, we provide a few types for them. For $n_p=1$, the gravitational waveforms are mainly characterized by a black hole quasinormal mode ringing, irrespective of perturbation profiles given initially. However, for $n_p=3$, the waveforms depend strongly on the initial perturbation profiles. In other words, the gravitational waveforms strongly depend on the stellar configuration and, in turn, on the ad hoc choice of the functional form of the perturbation in the case of supermassive stars.Comment: 31 pages, accepted for publication in Phys. Rev. D, typos and minor errors correcte

Signatures of the sources in the gravitational waves of a perturbed Schwarzschild black hole

The explicit form of perturbation equation for the $\Psi_4$ Weyl scalar, containing the matter source terms, is derived for general type D spacetimes. It is described in detail the particular case of the Schwarzschild spacetime using in-going penetrating coordinates. As a practical application, we focused on the emission of gravitational waves when a black hole is perturbed by a surrounding dust-like fluid matter. The symmetries of the spacetime and the simplicity of the matter source allow, by means of a spherical harmonic decomposition, to study the problem by means of a one dimensional numerical code.Comment: 17 pages, 8 figure

Domain Wall Spacetimes: Instability of Cosmological Event and Cauchy Horizons

The stability of cosmological event and Cauchy horizons of spacetimes associated with plane symmetric domain walls are studied. It is found that both horizons are not stable against perturbations of null fluids and massless scalar fields; they are turned into curvature singularities. These singularities are light-like and strong in the sense that both the tidal forces and distortions acting on test particles become unbounded when theses singularities are approached.Comment: Latex, 3 figures not included in the text but available upon reques

Podoconiosis, trachomatous trichiasis and cataract in northern Ethiopia: a comparative cross-sectional study

Background: Rural populations in low-income countries commonly suffer from the co-morbidity of neglected tropical diseases (NTDs). Podoconiosis, trachomatous trichiasis (both NTDs) and cataract are common causes of morbidity among subsistence farmers in the highlands of northern Ethiopia. We explored whether podoconiosis was associated with cataract or trachomatous trichiasis (TT) among this population. Methods: A comparative cross-sectional study was conducted in East Gojam region, Amhara, Ethiopia in May 2016 . Data were collected from patients previously identified as having podoconiosis and from matched healthy neighbourhood controls. Information on socio- demographic factors, clinical factors and past medical history were collected by an interview-administered questionnaire. Clinical examination involved grading of podoconiosis by examination of both legs, measurement of visual acuity, direct ophthalmoscopy of dilated pupils to grade cataract, and eyelid and corneal examination to grade trachoma. Multiple logistic regression was conducted to estimate independent association and correlates of podoconiosis, TT and cataract. Findings: A total of 700 participants were included in this study; 350 podoconiosis patients and 350 healthy neighbourhood controls. The prevalence of TT was higher among podoconiosis patients than controls (65 (18.6%) vs 43 (12.3%)) with an adjusted odds ratio (OR) 1.55 (95% Confidence Interval (CI) 1.12 - 2.11), p=0.05. There was no significant difference in 3 prevalence of cataract between the two populations with an adjusted OR 0.83 (95% CI 0.55-1.38), p=0.37. Mean best visual acuity was 0.59 (SD +/- 0.06) in podoconiosis cases compared to 0.44 (SD +/- 0.04) in controls, p=< 0.001. The proportion of patients classified as blind was higher in podoconiosis cases compared with healthy controls; 5.6% vs 2.0%; adjusted OR 2.63 (1.08-6.39), P = 0.03. Conclusions Individuals with podoconiosis have a higher burden of TT and worse visual acuity than their matched healthy neighbourhood controls. Further research into the environmental and biological reasons for this co-morbidity is required. A shared approach to managing these two NTDs within the same population could be beneficial

Spinor condensates and light scattering from Bose-Einstein condensates

These notes discuss two aspects of the physics of atomic Bose-Einstein condensates: optical properties and spinor condensates. The first topic includes light scattering experiments which probe the excitations of a condensate in both the free-particle and phonon regime. At higher light intensity, a new form of superradiance and phase-coherent matter wave amplification were observed. We also discuss properties of spinor condensates and describe studies of ground--state spin domain structures and dynamical studies which revealed metastable excited states and quantum tunneling.Comment: 58 pages, 33 figures, to appear in Proceedings of Les Houches 1999 Summer School, Session LXXI