29 research outputs found
A Time-Like Naked Singularity
We construct a class of spherically symmetric collapse models in which a
naked singularity may develop as the end state of collapse. The matter
distribution considered has negative radial and tangential pressures, but the
weak energy condition is obeyed throughout. The singularity forms at the center
of the collapsing cloud and continues to be visible for a finite time. The
duration of visibility depends on the nature of energy distribution. Hence the
causal structure of the resulting singularity depends on the nature of the mass
function chosen for the cloud. We present a general model in which the naked
singularity formed is timelike, neither pointlike nor null. Our work represents
a step toward clarifying the necessary conditions for the validity of the
Cosmic Censorship Conjecture.Comment: 4 pages, Revtex4, To appear in Physical Review
On the invariant causal characterization of singularities in spherically symmetric spacetimes
The causal character of singularities is often studied in relation to the
existence of naked singularities and the subsequent possible violation of the
cosmic censorship conjecture. Generally one constructs a model in the framework
of General Relativity described in some specific coordinates and finds an ad
hoc procedure to analyze the character of the singularity. In this article we
show that the causal character of the zero-areal-radius (R=0) singularity in
spherically symmetric models is related with some specific invariants. In this
way, if some assumptions are satisfied, one can ascertain the causal character
of the singularity algorithmically through the computation of these invariants
and, therefore, independently of the coordinates used in the model.Comment: A misprint corrected in Theor. 4.1 /Cor. 4.
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
New mathematical framework for spherical gravitational collapse
A theorem, giving necessary and sufficient condition for naked singularity
formation in spherically symmetric non static spacetimes under hypotheses of
physical acceptability, is formulated and proved. The theorem relates existence
of singular null geodesics to existence of regular curves which are
super-solutions of the radial null geodesic equation, and allows us to treat
all the known examples of naked singularities from a unified viewpoint. New
examples are also found using this approach, and perspectives are discussed.Comment: 8 pages, LaTeX2
The repulsive nature of naked singularities from the point of view of Quantum Mechanics
We use the Dirac equation coupled to a background metric to examine what
happens to quantum mechanical observables like the probability density and the
radial current in the vicinity of a naked singularity of the
Reissner-Nordstr\"{o}m type. We find that the wave function of the Dirac
particle is regular in the point of the singularity. We show that the
probability density is exactly zero at the singularity reflecting
quantum-mechanically the repulsive nature of the naked singularity.
Furthermore, the surface integral of the radial current over a sphere in the
vicinity of the naked singularity turns out to be also zero.Comment: 11 page
On the genericity of spacetime singularities
We consider here the genericity aspects of spacetime singularities that occur
in cosmology and in gravitational collapse. The singularity theorems (that
predict the occurrence of singularities in general relativity) allow the
singularities of gravitational collapse to be either visible to external
observers or covered by an event horizon of gravity. It is shown that the
visible singularities that develop as final states of spherical collapse are
generic. Some consequences of this fact are discussed.Comment: 19 pages, To be published in the Raychaudhuri Volume, eds. Naresh
Dadhich, Pankaj Joshi and Probir Ro
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 . 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
Spherically symmetric dissipative anisotropic fluids: A general study
The full set of equations governing the evolution of self--gravitating
spherically symmetric dissipative fluids with anisotropic stresses is deployed
and used to carry out a general study on the behaviour of such systems, in the
context of general relativity. Emphasis is given to the link between the Weyl
tensor, the shear tensor, the anisotropy of the pressure and the density
inhomogeneity. In particular we provide the general, necessary and sufficient,
condition for the vanishing of the spatial gradients of energy density, which
in turn suggests a possible definition of a gravitational arrow of time. Some
solutions are also exhibited to illustrate the discussion.Comment: 28 pages Latex. To appear in Phys.Rev.