Relativistic, Spherically Symmetric Star Clusters.IV. a Sufficient Condition for Instability of Isotropic Clusters against Radial Perturbations

1970 ◽  
Vol 160 ◽  
pp. 859 ◽  
Author(s):  
Edward D. Fackerell
Keyword(s):  
Spherically Symmetric ◽  
Sufficient Condition ◽  
Symmetric Star

Relativistic, Spherically Symmetric Star Clusters. III. Stability of Compact Isotropic Models

1969 ◽  
Vol 158 ◽  
pp. 17 ◽  
Author(s):  
James R. Ipser
Keyword(s):  
Star Clusters ◽  
Spherically Symmetric ◽  
Symmetric Star

Odd-parity perturbations of spherically symmetric star clusters in general relativity

1981 ◽  
Vol 247 ◽  
pp. 671 ◽  
Author(s):  
R. Semenzato ◽  
J. R. Ipser
Keyword(s):  
General Relativity ◽  
Star Clusters ◽  
Spherically Symmetric ◽  
Symmetric Star

scholarly journals EXPANSIONFREE FLUID EVOLUTION AND SKRIPKIN MODEL IN f(R) THEORY

2011 ◽  
Vol 20 (11) ◽  
pp. 2239-2252 ◽  
Author(s):  
M. SHARIF ◽  
H. RIZWANA KAUSAR
Keyword(s):  
General Relativity ◽  
The Self ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Dynamical Equations ◽  
Constant Energy ◽  
Isotropic Pressure ◽  
Symmetric Star ◽  
Constant Energy Density ◽  
General Influence

We consider the modified f(R) theory of gravity whose higher-order curvature terms are interpreted as a gravitational fluid or dark source. The gravitational collapse of a spherically symmetric star, made up of locally anisotropic viscous fluid, is studied under the general influence of the curvature fluid. Dynamical equations and junction conditions are modified in the context of f(R) dark energy and by taking into account the expansionfree evolution of the self-gravitating fluid. As a particular example, the Skripkin model is investigated which corresponds to isotropic pressure with constant energy density. The results are compared with corresponding results in General Relativity.

Gravitational collapse of dark matter interacting with dark energy: Black hole formation

2017 ◽  
Vol 26 (13) ◽  
pp. 1750142 ◽  
Author(s):  
Hasrat Hussain Shah ◽  
Quaid Iqbal
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Dark Energy ◽  
Gravitational Collapse ◽  
Anisotropic Pressure ◽  
Spherically Symmetric ◽  
Hole Formation ◽  
White Hole ◽  
De Formula ◽  
Symmetric Star

In this work, we study the gravitational collapsing process of a spherically symmetric star constitute of Dark Matter (DM), [Formula: see text], and Dark Energy (DE) [Formula: see text]. In this model, we use anisotropic pressure with Equation of State (EoS) [Formula: see text] and [Formula: see text], [Formula: see text]. It reveals that gravitational collapse of DM and DE with interaction leads to the formation of the black hole. When [Formula: see text] (phantoms), dust and phantoms could be ejected from the death of white hole. This emitted matter again undergoes to collapsing process and becomes the black hole. This study gives the generalization for isotropy of pressure in the fluid to anisotropy when there will be interaction between DM and DE.

scholarly journals A Class of Spherical and Elliptical Distributions with Gaussian-Like Limit Properties

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Chris Sherlock ◽  
Daniel Elton
Keyword(s):  
Functional Form ◽  
Marginal Distribution ◽  
Random Variables ◽  
Spherically Symmetric ◽  
Sufficient Condition ◽  
Elliptical Distributions ◽  
Symmetric Distributions ◽  
One Dimensional ◽  
Elliptically Symmetric Distributions

We present a class of spherically symmetric random variables defined by the property that as dimension increases to infinity the mass becomes concentrated in a hyperspherical shell, the width of which is negligible compared to its radius. We provide a sufficient condition for this property in terms of the functional form of the density and then show that the property carries through to equivalent elliptically symmetric distributions, provided that the contours are not too eccentric, in a sense which we make precise. Individual components of such distributions possess a number of appealing Gaussian-like limit properties, in particular that the limiting one-dimensional marginal distribution along any component is Gaussian.

On the collapse of a spherically symmetric star

1995 ◽  
Vol 36 (7) ◽  
pp. 3676-3693 ◽  
Author(s):  
Marcus Kriele
Keyword(s):  
Spherically Symmetric ◽  
Symmetric Star
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