17,962 research outputs found

### Quasi-spherical gravitational collapse and the role of initial data, anisotropy and inhomogeneity

In this paper, the role of anisotropy and inhomogeneity has been studied in
quasi-spherical gravitational collapse. Also the role of initial data has been
investigated in characterizing the final state of collapse. Finally, a linear
transformation on the initial data set has been presented and its impact has
been discussed.Comment: RevTex, 7 Latex pages, No figure

### Genericity aspects in gravitational collapse to black holes and naked singularities

We investigate here the genericity and stability aspects for naked
singularities and black holes that arise as the final states for a complete
gravitational collapse of a spherical massive matter cloud. The form of the
matter considered is a general Type I matter field, which includes most of the
physically reasonable matter fields such as dust, perfect fluids and such other
physically interesting forms of matter widely used in gravitation theory. We
first study here in some detail the effects of small pressure perturbations in
an otherwise pressure-free collapse scenario, and examine how a collapse
evolution that was going to the black hole endstate would be modified and go to
a naked singularity, once small pressures are introduced in the initial data.
This allows us to understand the distribution of black holes and naked
singularities in the initial data space. Collapse is examined in terms of the
evolutions allowed by Einstein equations, under suitable physical conditions
and as evolving from a regular initial data. We then show that both black holes
and naked singularities are generic outcomes of a complete collapse, when
genericity is defined in a suitable sense in an appropriate space.Comment: 24 pages, 6 figures, some changes in text and figures to match the
version accepted for publication by IJMP

### On the global visibility of singularity in quasi-spherical collapse

We analyze here the issue of local versus the global visibility of a
singularity that forms in gravitational collapse of a dust cloud, which has
important implications for the weak and strong versions of the cosmic
censorship hypothesis. We find conditions as to when a singularity will be only
locally naked, rather than being globally visible, thus preseving the weak
censorship hypothesis. The conditions for formation of a black hole or naked
singularity in the Szekeres quasi-spherical collapse models are worked out. The
causal behaviour of the singularity curve is studied by examining the outgoing
radial null geodesics, and the final outcome of collapse is related to the
nature of the regular initial data specified on an initial hypersurface from
which the collapse evolves. An interesting feature that emerges is the
singularity in Szekeres spacetimes can be ``directionally naked''.Comment: Latex file, 32 pages, 12 postscript figures. To appear in the Journal
of General Relativity and Gravitatio

### The Final Fate of Spherical Inhomogeneous Dust Collapse

We examine the role of the initial density and velocity distribution in the
gravitational collapse of a spherical inhomogeneous dust cloud. Such a collapse
is described by the Tolman-Bondi metric which has two free functions: the
`mass-function' and the `energy function', which are determined by the initial
density and velocity profile of the cloud. The collapse can end in a black-hole
or a naked singularity, depending on the initial parameters characterizing
these profiles. In the marginally bound case, we find that the collapse ends in
a naked singularity if the leading non-vanishing derivative of the density at
the center is either the first one or the second one. If the first two
derivatives are zero, and the third derivative non-zero, the singularity could
either be naked or covered, depending on a quantity determined by the third
derivative and the central density. If the first three derivatives are zero,
the collapse ends in a black hole. In particular, the classic result of
Oppenheimer and Snyder, that homogeneous dust collapse leads to a black hole,
is recovered as a special case. Analogous results are found when the cloud is
not marginally bound, and also for the case of a cloud starting from rest. We
also show how the strength of the naked singularity depends on the density and
velocity distribution. Our analysis generalizes and simplifies the earlier work
of Christodoulou and Newman [4,5] by dropping the assumption of evenness of
density functions. It turns out that relaxing this assumption allows for a
smooth transition from the naked singularity phase to the black-hole phase, and
also allows for the occurrence of strong curvature naked singularities.Comment: 23 pages; Plain Tex; TIFR-TAP preprin

### On trapped surface formation in gravitational collapse II

Further to our consideration on trapped surfaces in gravitational collapse,
where pressures were allowed to be negative while satisfying weak energy
condition to avoid trapped surface formation, we discuss here several other
attempts of similar nature in this direction. Certain astrophysical aspects are
pointed out towards examining the physical realization of such a possibility in
realistic gravitational collapse

### Gravitational collapse of an isentropic perfect fluid with a linear equation of state

We investigate here the gravitational collapse end states for a spherically
symmetric perfect fluid with an equation of state $p=k\rho$. It is shown that
given a regular initial data in terms of the density and pressure profiles at
the initial epoch from which the collapse develops, the black hole or naked
singularity outcomes depend on the choice of rest of the free functions
available, such as the velocities of the collapsing shells, and the dynamical
evolutions as allowed by Einstein equations. This clarifies the role that
equation of state and initial data play towards determining the final fate of
gravitational collapse.Comment: 7 Pages, Revtex4, To appear in Classical and Quantum Gravit

### Role of initial data in spherical collapse

We bring out here the role of initial data in causing the black hole and
naked singularity phases as the final end state of a continual gravitational
collapse. The collapse of a type I general matter field is considered, which
includes most of the known physical forms of matter. It is shown that given the
distribution of the density and pressure profiles at the initial surface from
which the collapse evolves, there is a freedom in choosing rest of the free
functions, such as the velocities of the collapsing shells, so that the end
state could be either a black hole or a naked singularity depending on this
choice. It is thus seen that it is the initial data that determines the end
state of spherical collapse in terms of these outcomes, and we get a good
picture of how these phases come about.Comment: 5 pages, Revtex4, Revised version, To appear in Physical Review

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