We present a new covariant and gauge-invariant perturbation formalism for dealing with spacetimes having spherical symmetry (or some preferred spatial direction) in the background, and apply it to the case of gravitational wave propagation in a Schwarzschild black hole spacetime. The 1+3 covariant approach is extended to a '1+1+2 covariant sheet' formalism by introducing a radial unit vector in addition to the timelike congruence, and decomposing all covariant quantities with respect to this. The background Schwarzschild solution is discussed and a covariant characterisation is given. We give the full first-order system of linearised 1+1+2 covariant equations, and we show how, by introducing (time and spherical) harmonic functions, these may be reduced to a system of first-order ordinary differential equations and algebraic constraints for the 1+1+2 variables which may be solved straightforwardly. We show how both the odd and even parity perturbations may be unified by the discovery of a covariant, frame-and gauge-invariant, transverse-traceless tensor describing gravitational waves, which satisfies a covariant wave equation equivalent to the ReggeWheeler equation for both even and odd parity perturbations. We show how the Zerilli equation may be derived from this tensor, and derive a similar transverse traceless tensor equivalent to this equation. The so-called 'special' quasinormal modes with purely imaginary frequency emerge naturally. The significance of the degrees of freedom in the choice of the two frame vectors is discussed, and we demonstrate that, for a certain frame choice, the underlying dynamics is governed purely by the Regge-Wheeler tensor. The two transverse-traceless Weyl tensors which carry the curvature of gravitational waves are discussed, and we give the closed system of four first-order ordinary differential equations describing their propagation. Finally, we consider the extension of this work to the study of gravitational waves in other astrophysical situations.

We demonstrate that the high isotropy of the Cosmic Microwave Background (CMB), combined with the Copernican principle, is not sufficient to prove homogeneity of the universe -in contrast to previous results on this subject. The crucial additional factor not included in earlier work is the acceleration of the fundamental observers. We find the complete class of irrotational perfect fluid spacetimes admitting an exactly isotropic radiation field for every fundamental observer and show that they are Friedman-Lemaître-Robertson-Walker (FLRW) if and only if the acceleration is zero. While inhomogeneous in general, these spacetimes all possess three-dimensional symmetry groups, from which it follows that they also admit a thermodynamic interpretation.In addition to perfect fluid models we also consider multi-component fluids containing non-interacting radiation, dust and a quintessential scalar field or cosmological constant in which the radiation is isotropic for the geodesic (dust) observers. It is shown that the non-acceleration of the fundamental observers forces these spacetimes to be FLRW.While it is plausible that fundamental observers (galaxies) in the real universe follow geodesics, it is strictly necessary to determine this from local observations for the cosmological principle to be more than an assumption. We discuss how observations may be used to test this.

We challenge the widely held belief that the cosmological principle is an obvious consequence of the observed isotropy of the cosmic microwave background radiation (CMB), combined with the Copernican principle. We perform a detailed analysis of a class of inhomogeneous perfect fluid cosmologies admitting an isotropic radiation field, with a view to assessing their viability as models of the real universe. These spacetimes are distinguished from FLRW universes by the presence of inhomogeneous pressure, which results in an acceleration of the fluid (fundamental observers). We examine their physical, geometrical and observational characteristics for all observer positions in the spacetimes. To this end, we derive exact, analytic expressions for the distance-redshift relations and anisotropies for any observer, and compare their predictions with available observational constraints. As far as the authors are aware, this work represents the first exact analysis of the observational properties of an inhomogeneous cosmological model for all observer positions. Considerable attention is devoted to the anisotropy in the CMB. The difficulty of defining the surface of last scattering in exact, inhomogenous cosmological models is discussed; several alternative practical definitions are presented, and one of these is used to estimate the CMB anisotropy for any model. The isotropy constraints derived from 'local' observations (redshift < ∼ 1) are also considered, qualitatively. A crucial aspect of this work is the application of the Copernican principle: for a specific model to be acceptable we demand that it must be consistent with current observational constraints (especially anisotropy constraints) for all observer locations. The most important results of the paper are presented as exclusion plots in the 2-D parameter space of the models. We show that there is a region of parameter space not ruled out by the constraints we consider and containing models that are significantly inhomogeneous. It follows immediately from this that the cosmological principle cannot be assumed to hold on the basis of present observational constraints. *

Abstract. We present a method for tracking solar photospheric flows that is highly efficient, and demonstrate it using high resolution MDI continuum images. The method involves making a surface from the photospheric granulation data, and allowing many small floating tracers or balls to be moved around by the evolving granulation pattern. The results are tested against synthesised granulation with known flow fields and compared to the results produced by Local Correlation tracking (LCT). The results from this new method have similar accuracy to those produced by LCT. We also investigate the maximum spatial and temporal resolution of the velocity field that it is possible to extract, based on the statistical properties of the granulation data. We conclude that both methods produce results that are close to the maximum resolution possible from granulation data. The code runs very significantly faster than our similarly optimised LCT code, making real time applications on large data sets possible. The tracking method is not limited to photospheric flows, and will also work on any velocity field where there are visible moving features of known scale length.

A two-dimensional particle code that simulates electrical breakdown of gases by modeling avalanche evolution from the initial ion-electron pair up to the development of a streamer is presented. Trajectories of individual particles are followed, the self-field is included consistently and collision processes are accurately modeled using experimentally determined cross sections. It is emphasized that the tadpolelike structure of well-formed streamer heads is present throughout the avalanche phase, and that the transition to the self-similar evolution characteristic of the streamer phase merely reflects the continued development of this structure. The importance of this for conventional fluid simulations of streamers, where the initial conditions for the streamer are taken to be a structureless Gaussian concentration of neutral plasma with significant density, is discussed. In the (realistic) situation where several avalanches are present simultaneously the large self-fields that rapidly develop lead to a strong interaction between them, in accord with the standard "cartoon" of streamer evolution.