11 research outputs found
Relativistic dynamics of cylindrical shells of counter-rotating particles
Although infinite cylinders are not astrophysical entities, it is possible to
learn a great deal about the basic qualitative features of generation of
gravitational waves and the behavior of the matter conforming such shells in
the limits of very small radius. We describe the analytical model using kinetic
theory for the matter and the junction conditions through the shell to obtain
its equation of motion. The nature of the static solutions are analyzed, both
for a single shell as well as for two concentric shells. In this second case,
for a time dependent external shell, we integrate numerically the equation of
motion for several values of the constants of the system. Also, a brief
description in terms of the Komar mass is given to account for the
gravitational wave energy emitted by the system.Comment: 19 pages, 8 figure
Gravitational Collapse: Expanding and Collapsing Regions
We investigate the expanding and collapsing regions by taking two well-known
spherically symmetric spacetimes. For this purpose, the general formalism is
developed by using Israel junction conditions for arbitrary spacetimes. This
has been used to obtain the surface energy density and the tangential pressure.
The minimal pressure provides the gateway to explore the expanding and
collapsing regions. We take Minkowski and Kantowski-Sachs spacetimes and use
the general formulation to investigate the expanding and collapsing regions of
the shell.Comment: 12 pages, 4 figures, accepted for publication in Gen. Relativ. Gra
Critical Collapse of Cylindrically Symmetric Scalar Field in Four-Dimensional Einstein's Theory of Gravity
Four-dimensional cylindrically symmetric spacetimes with homothetic
self-similarity are studied in the context of Einstein's Theory of Gravity, and
a class of exact solutions to the Einstein-massless scalar field equations is
found. Their local and global properties are investigated and found that they
represent gravitational collapse of a massless scalar field. In some cases the
collapse forms black holes with cylindrical symmetry, while in the other cases
it does not. The linear perturbations of these solutions are also studied and
given in closed form. From the spectra of the unstable eigen-modes, it is found
that there exists one solution that has precisely one unstable mode, which may
represent a critical solution, sitting on a boundary that separates two
different basins of attraction in the phase space.Comment: Some typos are corrected. The final version to appear in Phys. Rev.
Naked singularities in cylindrical collapse of counterrotating dust shells
Solutions describing the gravitational collapse of asymptotically flat cylindrical and prolate shells of (null) dust are shown to admit globally naked singularities
Expanding and Collapsing Scalar Field Thin Shell
This paper deals with the dynamics of scalar field thin shell in the
Reissner-Nordstrm geometry. The Israel junction conditions between
Reissner-Nordstrm spacetimes are derived, which lead to the equation
of motion of scalar field shell and Klien-Gordon equation. These equations are
solved numerically by taking scalar field model with the quadratic scalar
potential. It is found that solution represents the expanding and collapsing
scalar field shell. For the better understanding of this problem, we
investigate the case of massless scalar field (by taking the scalar field
potential zero). Also, we evaluate the scalar field potential when is an
explicit function of . We conclude that both massless as well as massive
scalar field shell can expand to infinity at constant rate or collapse to zero
size forming a curvature singularity or bounce under suitable conditions.Comment: 15 pages, 11 figure
Gravitational Collapse of Cylindrical Shells Made of Counter-Rotating Dust Particles
The general formulas of a non-rotating dynamic thin shell that connects two
arbitrary cylindrical regions are given using Israel's method. As an
application of them, the dynamics of a thin shell made of counter-rotating dust
particles, which emits both gravitational waves and massless particles when it
is expanding or collapsing, is studied. It is found that when the models
represent a collapsing shell, in some cases the angular momentum of the dust
particles is strong enough to halt the collapse, so that a spacetime
singularity is prevented from forming, while in other cases it is not, and a
line-like spacetime singularity is finally formed on the symmetry axis.Comment: To appear in Phys. Rev.
High-Speed Cylindrical Collapse of Two Perfect Fluids
In this paper, the study of the gravitational collapse of cylindrically
distributed two perfect fluid system has been carried out. It is assumed that
the collapsing speeds of the two fluids are very large. We explore this
condition by using the high-speed approximation scheme. There arise two cases,
i.e., bounded and vanishing of the ratios of the pressures with densities of
two fluids given by . It is shown that the high-speed approximation
scheme breaks down by non-zero pressures when are bounded
below by some positive constants. The failure of the high-speed approximation
scheme at some particular time of the gravitational collapse suggests the
uncertainity on the evolution at and after this time. In the bounded case, the
naked singularity formation seems to be impossible for the cylindrical two
perfect fluids. For the vanishing case, if a linear equation of state is used,
the high-speed collapse does not break down by the effects of the pressures and
consequently a naked singularity forms. This work provides the generalisation
of the results already given by Nakao and Morisawa [1] for the perfect fluid.Comment: 11 pages, 1 figure, accepted for publication in Gen. Rel. Gra
Star Models with Dark Energy
We have constructed star models consisting of four parts: (i) a homogeneous
inner core with anisotropic pressure (ii) an infinitesimal thin shell
separating the core and the envelope; (iii) an envelope of inhomogeneous
density and isotropic pressure; (iv) an infinitesimal thin shell matching the
envelope boundary and the exterior Schwarzschild spacetime. We have analyzed
all the energy conditions for the core, envelope and the two thin shells. We
have found that, in order to have static solutions, at least one of the regions
must be constituted by dark energy. The results show that there is no physical
reason to have a superior limit for the mass of these objects but for the ratio
of mass and radius.Comment: 20 pages, 1 figure, references and some comments added, typos
corrected, in press GR