82 research outputs found
Transverse frames for Petrov type I spacetimes: a general algebraic procedure
We develop an algebraic procedure to rotate a general Newman-Penrose tetrad
in a Petrov type I spacetime into a frame with Weyl scalars and
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 and
to zero makes apparent the superposition of a Coulomb-type effect
with transverse degrees of freedom and .Comment: 10 pages, submitted to Classical Quantum Gravit
The Kelvin-Helmholtz Instability in an Expanding Universe and its Effect on Dark Matter
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
A Concise Introduction to Perturbation Theory in Cosmology
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
Regular spherical dust spacetimes
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
Exact non-equilibrium solutions of the Einstein-Boltzmann equations. II
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
Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?
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
Anisotropic Observations in Universes with Nonlinear Inhomogeneity
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
Anisotropy in Bianchi-type brane cosmologies
The behavior near the initial singular state of the anisotropy parameter of
the arbitrary type, homogeneous and anisotropic Bianchi models is considered in
the framework of the brane world cosmological models. The matter content on the
brane is assumed to be an isotropic perfect cosmological fluid, obeying a
barotropic equation of state. To obtain the value of the anisotropy parameter
at an arbitrary moment an evolution equation is derived, describing the
dynamics of the anisotropy as a function of the volume scale factor of the
Universe. The general solution of this equation can be obtained in an exact
analytical form for the Bianchi I and V types and in a closed form for all
other homogeneous and anisotropic geometries. The study of the values of the
anisotropy in the limit of small times shows that for all Bianchi type
space-times filled with a non-zero pressure cosmological fluid, obeying a
linear barotropic equation of state, the initial singular state on the brane is
isotropic. This result is obtained by assuming that in the limit of small times
the asymptotic behavior of the scale factors is of Kasner-type. For brane
worlds filled with dust, the initial values of the anisotropy coincide in both
brane world and standard four-dimensional general relativistic cosmologies.Comment: 12 pages, no figures, to appear in Class. Quantum Gra
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