2,146 research outputs found
General properties of cosmological models with an Isotropic Singularity
Much of the published work regarding the Isotropic Singularity is performed
under the assumption that the matter source for the cosmological model is a
barotropic perfect fluid, or even a perfect fluid with a -law equation
of state. There are, however, some general properties of cosmological models
which admit an Isotropic Singularity, irrespective of the matter source. In
particular, we show that the Isotropic Singularity is a point-like singularity
and that vacuum space-times cannot admit an Isotropic Singularity. The
relationships between the Isotropic Singularity, and the energy conditions, and
the Hubble parameter is explored. A review of work by the authors, regarding
the Isotropic Singularity, is presented.Comment: 18 pages, 1 figur
A Phase Space Approach to Gravitational Enropy
We examine the definition S = ln Omega as a candidate "gravitational entropy"
function. We calculate its behavior for gravitationl and density perturbations
in closed, open and flat cosmologies and find that in all cases it increases
monotonically. Using the formalism to calculate the gravitational entropy
produced during inflation gives the canonical answer. We compare the behavior
of S with the behavior of the square of the Weyl tensor. Applying the formalism
to black holes has proven more problematical.Comment: Talk delivered at South African Relativistic Cosmology Symposium, Feb
1999. Some new results over Rothman and Anninos 97. To appear in GRG, 17
page
Gravitational Entropy and Quantum Cosmology
We investigate the evolution of different measures of ``Gravitational
Entropy'' in Bianchi type I and Lema\^itre-Tolman universe models.
A new quantity behaving in accordance with the second law of thermodynamics
is introduced. We then go on and investigate whether a quantum calculation of
initial conditions for the universe based upon the Wheeler-DeWitt equation
supports Penrose's Weyl Curvature Conjecture, according to which the Ricci part
of the curvature dominates over the Weyl part at the initial singularity of the
universe. The theory is applied to the Bianchi type I universe models with dust
and a cosmological constant and to the Lema\^itre-Tolman universe models. We
investigate two different versions of the conjecture. First we investigate a
local version which fails to support the conjecture. Thereafter we construct a
non-local entity which shows more promising behaviour concerning the
conjecture.Comment: 20 pages, 7 ps figure
Measures of gravitational entropy I. Self-similar spacetimes
We examine the possibility that the gravitational contribution to the entropy
of a system can be identified with some measure of the Weyl curvature. In this
paper we consider homothetically self-similar spacetimes. These are believed to
play an important role in describing the asymptotic properties of more general
models. By exploiting their symmetry properties we are able to impose
significant restrictions on measures of the Weyl curvature which could reflect
the gravitational entropy of a system. In particular, we are able to show, by
way of a more general relation, that the most widely used "dimensionless"
scalar is \textit{not} a candidate for this measure along homothetic
trajectories.Comment: revtex, minor clarifications, to appear in Physical Review
Apparent horizons in the quasi-spherical Szekeres models
The notion of an apparent horizon (AH) in a collapsing object can be carried
over from the Lema\^{\i}tre -- Tolman (L--T) to the quasispherical Szekeres
models in three ways: 1. Literally by the definition -- the AH is the boundary
of the region, in which every bundle of null geodesics has negative expansion
scalar. 2. As the locus, at which null lines that are as nearly radial as
possible are turned toward decreasing areal radius . These lines are in
general nongeodesic. The name "absolute apparent horizon" (AAH) is proposed for
this locus. 3. As the boundary of a region, where null \textit{geodesics} are
turned toward decreasing . The name "light collapse region" (LCR) is
proposed for this region (which is 3-dimensional in every space of constant
); its boundary coincides with the AAH. The AH and AAH coincide in the L--T
models. In the quasispherical Szekeres models, the AH is different from (but
not disjoint with) the AAH. Properties of the AAH and LCR are investigated, and
the relations between the AAH and the AH are illustrated with diagrams using an
explicit example of a Szekeres metric. It turns out that an observer who is
already within the AH is, for some time, not yet within the AAH. Nevertheless,
no light signal can be sent through the AH from the inside. The analogue of the
AAH for massive particles is also considered.Comment: 14 pages, 9 figures, includes little extensions and style corrections
made after referee's comments, the text matches the published versio
A note on behaviour at an isotropic singularity
The behaviour of Jacobi fields along a time-like geodesic running into an
isotropic singularity is studied. It is shown that the Jacobi fields are
crushed to zero length at a rate which is the same in every direction
orthogonal to the geodesic. We show by means of a counter-example that this
crushing effect depends crucially on a technicality of the definition of
isotropic singularities, and not just on the uniform degeneracy of the metric
at the singularity.Comment: 13 pp. plain latex. To appear in Classical and Quantum Gravit
Isotropic cosmological singularities: other matter models
Isotropic cosmological singularities are singularities which can be removed
by rescaling the metric. In some cases already studied (gr-qc/9903008,
gr-qc/9903009, gr-qc/9903018) existence and uniqueness of cosmological models
with data at the singularity has been established. These were cosmologies with,
as source, either perfect fluids with linear equations of state or massless,
collisionless particles. In this article we consider how to extend these
results to a variety of other matter models. These are scalar fields, massive
collisionless matter, the Yang-Mills plasma of Choquet-Bruhat, or matter
satisfying the Einstein-Boltzmann equation.Comment: LaTeX, 19 pages, no figure
Geometry of the quasi-hyperbolic Szekeres models
Geometric properties of the quasi-hyperbolic Szekeres models are discussed
and related to the quasi-spherical Szekeres models. Typical examples of shapes
of various classes of 2-dimensional coordinate surfaces are shown in graphs;
for the hyperbolically symmetric subcase and for the general quasi-hyperbolic
case. An analysis of the mass function is carried out in parallel to an
analogous analysis for the quasi-spherical models. This leads to the conclusion
that determines the density of rest mass averaged over the whole space
of constant time.Comment: 19 pages, 13 figures. This version matches the published tex
The growth of structure in the Szekeres inhomogeneous cosmological models and the matter-dominated era
This study belongs to a series devoted to using Szekeres inhomogeneous models
to develop a theoretical framework where observations can be investigated with
a wider range of possible interpretations. We look here into the growth of
large-scale structure in the models. The Szekeres models are exact solutions to
Einstein's equations that were originally derived with no symmetries. We use a
formulation of the models that is due to Goode and Wainwright, who considered
the models as exact perturbations of an FLRW background. Using the Raychaudhuri
equation, we write for the two classes of the models, exact growth equations in
terms of the under/overdensity and measurable cosmological parameters. The new
equations in the overdensity split into two informative parts. The first part,
while exact, is identical to the growth equation in the usual linearly
perturbed FLRW models, while the second part constitutes exact non-linear
perturbations. We integrate numerically the full exact growth rate equations
for the flat and curved cases. We find that for the matter-dominated era, the
Szekeres growth rate is up to a factor of three to five stronger than the usual
linearly perturbed FLRW cases, reflecting the effect of exact Szekeres
non-linear perturbations. The growth is also stronger than that of the
non-linear spherical collapse model, and the difference between the two
increases with time. This highlights the distinction when we use general
inhomogeneous models where shear and a tidal gravitational field are present
and contribute to the gravitational clustering. Additionally, it is worth
observing that the enhancement of the growth found in the Szekeres models
during the matter-dominated era could suggest a substitute to the argument that
dark matter is needed when using FLRW models to explain the enhanced growth and
resulting large-scale structures that we observe today (abridged)Comment: 18 pages, 4 figures, matches PRD accepted versio
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