215 research outputs found
Spherically symmetric relativistic stellar structures
We investigate relativistic spherically symmetric static perfect fluid models
in the framework of the theory of dynamical systems. The field equations are
recast into a regular dynamical system on a 3-dimensional compact state space,
thereby avoiding the non-regularity problems associated with the
Tolman-Oppenheimer-Volkoff equation. The global picture of the solution space
thus obtained is used to derive qualitative features and to prove theorems
about mass-radius properties. The perfect fluids we discuss are described by
barotropic equations of state that are asymptotically polytropic at low
pressures and, for certain applications, asymptotically linear at high
pressures. We employ dimensionless variables that are asymptotically homology
invariant in the low pressure regime, and thus we generalize standard work on
Newtonian polytropes to a relativistic setting and to a much larger class of
equations of state. Our dynamical systems framework is particularly suited for
numerical computations, as illustrated by several numerical examples, e.g., the
ideal neutron gas and examples that involve phase transitions.Comment: 23 pages, 25 figures (compressed), LaTe
Perfect fluids and generic spacelike singularities
We present the conformally 1+3 Hubble-normalized field equations together
with the general total source equations, and then specialize to a source that
consists of perfect fluids with general barotropic equations of state.
Motivating, formulating, and assuming certain conjectures, we derive results
about how the properties of fluids (equations of state, momenta, angular
momenta) and generic spacelike singularities affect each other.Comment: Considerable changes have been made in presentation and arguments,
resulting in sharper conclusion
Asymptotic silence of generic cosmological singularities
In this letter we investigate the nature of generic cosmological
singularities using the framework developed by Uggla et al. We do so by
studying the past asymptotic dynamics of general vacuum G2 cosmologies, models
that are expected to capture the singular behavior of generic cosmologies with
no symmetries at all. In particular, our results indicate that asymptotic
silence holds, i.e., that particle horizons along all timelines shrink to zero
for generic solutions. Moreover, we provide evidence that spatial derivatives
become dynamically insignificant along generic timelines, and that the
evolution into the past along such timelines is governed by an asymptotic
dynamical system which is associated with an invariant set -- the silent
boundary. We also identify an attracting subset on the silent boundary that
organizes the oscillatory dynamics of generic timelines in the singular regime.
In addition, we discuss the dynamics associated with recurring spike formation.Comment: 4 pages, 5 *.eps figures, RevTeX4; replaced by significantly revised
version, to appear in Physical Review Letter
Homoclinic chaos and energy condition violation
In this letter we discuss the connection between so-called homoclinic chaos
and the violation of energy conditions in locally rotationally symmetric
Bianchi type IX models, where the matter is assumed to be non-tilted dust and a
positive cosmological constant. We show that homoclinic chaos in these models
is an artifact of unphysical assumptions: it requires that there exist
solutions with positive matter energy density that evolve through the
singularity and beyond as solutions with negative matter energy density
. Homoclinic chaos is absent when it is assumed that the dust particles
always retain their positive mass.In addition, we discuss more general models:
for solutions that are not locally rotionally symmetric we demonstrate that the
construction of extensions through the singularity, which is required for
homoclinic chaos, is not possible in general.Comment: 4 pages, RevTe
New explicit spike solution -- non-local component of the generalized Mixmaster attractor
By applying a standard solution-generating transformation to an arbitrary
vacuum Bianchi type II solution, one generates a new solution with spikes
commonly observed in numerical simulations. It is conjectured that the spike
solution is part of the generalized Mixmaster attractor.Comment: Significantly revised. Colour figures simplified to accommodate
non-colour printin
Conformal regularization of Einstein's field equations
To study asymptotic structures, we regularize Einstein's field equations by
means of conformal transformations. The conformal factor is chosen so that it
carries a dimensional scale that captures crucial asymptotic features. By
choosing a conformal orthonormal frame we obtain a coupled system of
differential equations for a set of dimensionless variables, associated with
the conformal dimensionless metric, where the variables describe ratios with
respect to the chosen asymptotic scale structure. As examples, we describe some
explicit choices of conformal factors and coordinates appropriate for the
situation of a timelike congruence approaching a singularity. One choice is
shown to just slightly modify the so-called Hubble-normalized approach, and one
leads to dimensionless first order symmetric hyperbolic equations. We also
discuss differences and similarities with other conformal approaches in the
literature, as regards, e.g., isotropic singularities.Comment: New title plus corrections and text added. To appear in CQ
General Relativistic 1+3 Orthonormal Frame Approach Revisited
The equations of the 1+3 orthonormal frame approach are explicitly presented
and discussed. Natural choices of local coordinates are mentioned. A
dimensionless formulation is subsequently given. It is demonstrated how one can
obtain a number of interesting problems by specializing the general equations.
In particular, equation systems for ``silent'' dust cosmological models also
containing magnetic Maxwell fields, locally rotationally symmetric spacetime
geometries and spatially homogeneous cosmological models are presented. We show
that while the 3-Cotton--York tensor is zero for Szekeres dust models, it is
nonzero for a generic representative within the ``silent'' class.Comment: 41 pages, uufiles encoded postscript file, submitted to Phys. Rev.
Exact Hypersurface-Homogeneous Solutions in Cosmology and Astrophysics
A framework is introduced which explains the existence and similarities of
most exact solutions of the Einstein equations with a wide range of sources for
the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian
formulation. This class includes the spatially homogeneous cosmological models
and the astrophysically interesting static spherically symmetric models as well
as the stationary cylindrically symmetric models. The framework involves
methods for finding and exploiting hidden symmetries and invariant submanifolds
of the Hamiltonian formulation of the field equations. It unifies, simplifies
and extends most known work on hypersurface-homogeneous exact solutions. It is
shown that the same framework is also relevant to gravitational theories with a
similar structure, like Brans-Dicke or higher-dimensional theories.Comment: 41 pages, REVTEX/LaTeX 2.09 file (don't use LaTeX2e !!!) Accepted for
publication in Phys. Rev.
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