531 research outputs found
Anisotropic Cosmological Models with Energy Density Dependent Bulk Viscosity
An analysis is presented of the Bianchi type I cosmological models with a
bulk viscosity when the universe is filled with the stiff fluid
while the viscosity is a power function of the energy density, such as . Although the exact solutions are obtainable only when the
is an integer, the characteristics of evolution can be clarified for the
models with arbitrary value of . It is shown that, except for the
model that has solutions with infinite energy density at initial state, the
anisotropic solutions that evolve to positive Hubble functions in the later
stage will begin with Kasner-type curvature singularity and zero energy density
at finite past for the models, and with finite Hubble functions and
finite negative energy density at infinite past for the models. In the
course of evolution, matters are created and the anisotropies of the universe
are smoothed out. At the final stage, cosmologies are driven to infinite
expansion state, de Sitter space-time, or Friedman universe asymptotically.
However, the de Sitter space-time is the only attractor state for the
models. The solutions that are free of cosmological singularity for any finite
proper time are singled out. The extension to the higher-dimensional models is
also discussed
Effects of the Shear Viscosity on the Character of Cosmological Evolution
Bianchi type I cosmological models are studied that contain a stiff fluid
with a shear viscosity that is a power function of the energy density, such as
. These models are analyzed by describing the
cosmological evolutions as the trajectories in the phase plane of Hubble
functions. The simple and exact equations that determine these flows are
obtained when is an integer. In particular, it is proved that there is no
Einstein initial singularity in the models of . Cosmologies are
found to begin with zero energy density and in the course of evolution the
gravitational field will create matter. At the final stage, cosmologies are
driven to the isotropic Fnedmann universe. It is also pointed out that although
the anisotropy will always be smoothed out asymptotically, there are solutions
that simultaneously possess non-positive and non-negative Hubble functions for
all time. This means that the cosmological dimensional reduction can work even
if the matter fluid having shear viscosity. These characteristics can also be
found in any-dimensional models
Rotating Black Holes on Kaluza-Klein Bubbles
Using the solitonic solution generating techniques, we generate a new exact
solution which describes a pair of rotating black holes on a Kaluza-Klein
bubble as a vacuum solution in the five-dimensional Kaluza-Klein theory. We
also investigate the properties of this solution. Two black holes with topology
S^3 are rotating along the same direction and the bubble plays a role in
holding two black holes. In static case, it coincides with the solution found
by Elvang and Horowitz.Comment: 16 pages, 1 figure, minor correctio
New Axisymmetric Stationary Solutions of Five-dimensional Vacuum Einstein Equations with Asymptotic Flatness
New axisymmetric stationary solutions of the vacuum Einstein equations in
five-dimensional asymptotically flat spacetimes are obtained by using solitonic
solution-generating techniques. The new solutions are shown to be equivalent to
the four-dimensional multi-solitonic solutions derived from particular class of
four-dimensional Weyl solutions and to include different black rings from those
obtained by Emparan and Reall.Comment: 6 pages, 3 figures;typos corrected, presentations improved,
references added;accepted versio
The Jeans Instability in Presence of Viscous Effects
An analysis of the gravitational instability in presence of dissipative
effects is addressed. In particular, the standard Jeans Mechanism and the
generalization in treating the Universe expansion are both analyzed when bulk
viscosity affects the first-order Newtonian dynamics. As results, the
perturbation evolution is founded to be damped by dissipative processes and the
top-down mechanism of structure fragmentation is suppressed. In such a scheme,
the value of the Jeans Mass remains unchanged also in presence of viscosity.Comment: 13 pages, 2 figure
Homogeneous and isotropic big rips?
We investigate the way big rips are approached in a fully inhomogeneous
description of the space-time geometry. If the pressure and energy densities
are connected by a (supernegative) barotropic index, the spatial gradients and
the anisotropic expansion decay as the big rip is approached. This behaviour is
contrasted with the usual big-bang singularities. A similar analysis is
performed in the case of sudden (quiescent) singularities and it is argued that
the spatial gradients may well be non-negligible in the vicinity of pressure
singularities.Comment: 8 page
Relationship Between Solitonic Solutions of Five-Dimensional Einstein Equations
We give the relation between the solutions generated by the inverse
scattering method and the B\"acklund transformation applied to the vacuum
five-dimensional Einstein equations. In particular, we show that the
two-solitonic solutions generated from an arbitrary diagonal seed by the
B\"acklund transformation are contained within those generated from the same
seed by the inverse scattering method.Comment: 17 pages, Some references are added, to be published in Phys.Rev.
On the Gravitational Collapse of a Gas Cloud in Presence of Bulk Viscosity
We analyze the effects induced by the bulk viscosity on the dynamics
associated to the extreme gravitational collapse. Aim of the work is to
investigate whether the presence of viscous corrections to the evolution of a
collapsing gas cloud influence the fragmentation process. To this end we study
the dynamics of a uniform and spherically symmetric cloud with corrections due
to the negative pressure contribution associated to the bulk viscosity
phenomenology. Within the framework of a Newtonian approach (whose range of
validity is outlined), we extend to the viscous case either the Lagrangian,
either the Eulerian motion of the system and we treat the asymptotic evolution
in correspondence to a viscosity coefficient of the form ( being the cloud density and ). We show how,
in the adiabatic-like behavior of the gas (i.e. when the politropic index takes
values ), density contrasts acquire, asymptotically, a
vanishing behavior which prevents the formation of sub-structures. We can
conclude that in the adiabatic-like collapse the top down mechanism of
structures formation is suppressed as soon as enough strong viscous effects are
taken into account. Such a feature is not present in the isothermal-like (i.e.
) collapse because the sub-structures formation is yet present
and outlines the same behavior as in the non-viscous case. We emphasize that in
the adiabatic-like collapse the bulk viscosity is also responsible for the
appearance of a threshold scale beyond which perturbations begin to increase.Comment: 13 pages, no figur
Bulk Viscosity Effects on the Early Universe Stability
We present a discussion of the effects induced by the bulk viscosity on the
very early Universe stability. The matter filling the cosmological (isotropic
and homogeneous) background is described by a viscous fluid having an
ultrarelativistic equation of state and whose viscosity coefficient is related
to the energy density via a power-law of the form . The
analytic expression of the density contrast (obtained for ) shows
that, for small values of the constant , its behavior is not
significantly different from the non-viscous one derived by E.M. Lifshitz. But
as soon as overcomes a critical value, the growth of the density
contrast is suppressed forward in time by the viscosity and the stability of
the Universe is favored in the expanding picture. On the other hand, in such a
regime, the asymptotic approach to the initial singularity (taken at ) is
deeply modified by the apparency of significant viscosity in the primordial
thermal bath i.e. the isotropic and homogeneous Universe admits an unstable
collapsing picture. In our model this feature regards also scalar perturbations
while in the non-viscous case it appears only for tensor modes.Comment: 8 pages, no figur
Chaos of Yang-Mills Field in Class A Bianchi Spacetimes
Studying Yang-Mills field and gravitational field in class A Bianchi
spacetimes, we find that chaotic behavior appears in the late phase (the
asymptotic future). In this phase, the Yang-Mills field behaves as that in
Minkowski spacetime, in which we can understand it by a potential picture,
except for the types VIII and IX. At the same time, in the initial phase (near
the initial singularity), we numerically find that the behavior seems to
approach the Kasner solution. However, we show that the Kasner circle is
unstable and the Kasner solution is not an attractor. From an analysis of
stability and numerical simulation, we find a Mixmaster-like behavior in
Bianchi I spacetime. Although this result may provide a counterexample to the
BKL (Belinskii, Khalatnikov and Lifshitz) conjecture, we show that the BKL
conjecture is still valid in Bianchi IX spacetime. We also analyze a
multiplicative effect of two types of chaos, that is, chaos with the Yang-Mills
field and that in vacuum Bianchi IX spacetime. Two types of chaos seem to
coexist in the initial phase. However, the effect due to the Yang-Mills field
is much smaller than that of the curvature term.Comment: 15 pages, 8 figure
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