103 research outputs found

    Transverse frames for Petrov type I spacetimes: a general algebraic procedure

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    We develop an algebraic procedure to rotate a general Newman-Penrose tetrad in a Petrov type I spacetime into a frame with Weyl scalars Ψ1\Psi_{1} and Ψ3\Psi_{3} equal to zero, assuming that initially all the Weyl scalars are non vanishing. The new frame highlights the physical properties of the spacetime. In particular, in a Petrov Type I spacetime, setting Ψ1\Psi_{1} and Ψ3\Psi_{3} to zero makes apparent the superposition of a Coulomb-type effect Ψ2\Psi_{2} with transverse degrees of freedom Ψ0\Psi_{0} and Ψ4\Psi_{4}.Comment: 10 pages, submitted to Classical Quantum Gravit

    The Kelvin-Helmholtz Instability in an Expanding Universe and its Effect on Dark Matter

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    We extend the Kelvin-Helmholtz instability to an expanding background. We study the evolution of a non-viscous irrotational fluid and find that for wavelengths much smaller than the Hubble scale small perturbations of the fluid are unstable for wavenumbers larger than a critical value. We then apply this result in the early universe, treating cold dark matter as a classical fluid with vanishing background pressure.Comment: 5 pages, 1 figure. v2 extended to cover density perturbations and now applies to both compressible and incompressible irrotational fluids. Clarified discussion. v3 typos corrected, extended discussio

    Regular spherical dust spacetimes

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    Physical (and weak) regularity conditions are used to determine and classify all the possible types of spherically symmetric dust spacetimes in general relativity. This work unifies and completes various earlier results. The junction conditions are described for general non-comoving (and non-null) surfaces, and the limits of kinematical quantities are given on all comoving surfaces where there is Darmois matching. We show that an inhomogeneous generalisation of the Kantowski-Sachs metric may be joined to the Lemaitre-Tolman-Bondi metric. All the possible spacetimes are explicitly divided into four groups according to topology, including a group in which the spatial sections have the topology of a 3-torus. The recollapse conjecture (for these spacetimes) follows naturally in this approach.Comment: Minor improvements, additional references. Accepted by GR

    A Concise Introduction to Perturbation Theory in Cosmology

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    We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive approach to calculating gauge transformations. We also construct gauge-invariant variables, including the second order tensor perturbation on uniform curvature hypersurfaces.Comment: revtex4, 16 pages, 3 figures; v2: minor changes, typos corrected, reference added, version accepted by CQ

    Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?

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    We use the Szekeres inhomogeneous relativistic models in order to fit supernova combined data sets. We show that with a choice of the spatial curvature function that is guided by current observations, the models fit the supernova data almost as well as the LCDM model without requiring a dark energy component. The Szekeres models were originally derived as an exact solution to Einstein's equations with a general metric that has no symmetries and are regarded as good candidates to model the true lumpy universe that we observe. The null geodesics in these models are not radial. The best fit model found is also consistent with the requirement of spatial flatness at CMB scales. The first results presented here seem to encourage further investigations of apparent acceleration using various inhomogeneous models and other constraints from CMB and large structure need to be explored next.Comment: 6 pages, 1 figure, matches version published in PR

    Exact non-equilibrium solutions of the Einstein-Boltzmann equations. II

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    We find exact solutions of the Einstein-Boltzmann equations with relaxational collision term in FRW and Bianchi I spacetimes. The kinematic and thermodynamic properties of the solutions are investigated. We give an exact expression for the bulk viscous pressure of an FRW distribution that relaxes towards collision-dominated equilibrium. If the relaxation is toward collision-free equilibrium, the bulk viscosity vanishes - but there is still entropy production. The Bianchi I solutions have zero heat flux and bulk viscosity, but nonzero shear viscosity. The solutions are used to construct a realisation of the Weyl Curvature Hypothesis.Comment: 16 pages LaTex, CQG documentstyle (ioplppt

    Anisotropic Observations in Universes with Nonlinear Inhomogeneity

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    We calculate the off--center observational relations in a spherically symmetric dust universe that is inhomogeneous at small redshifts. In contrast to the usual model, in which the CMBR dipole is interpreted as a Doppler effect due to peculiar velocity, our model explores an alternative interpretation, in which the CMBR dipole is non--Doppler, and the observer is comoving with the mean matter flow. We do not assume a background frame relative to which peculiar velocities are calculated. Our analysis is fully nonlinear and the density contrast is not assumed to be small. We obtain exact expressions for the Hubble and deceleration parameters, and find that both parameters have quadrupole anisotropies, but no dipoles. A simple numerical procedure for calculating the CMBR dipole anisotropy in our model is presented, and the observed 0.1% dipole is shown to be reproducible with a reasonable choices of parameters.Comment: 12 pages, Latex, 2 Maple graphs available from authors; submitted Ap
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