24,065 research outputs found
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
A characterization of the central shell-focusing singularity in spherical gravitational collapse
We give a characterization of the central shell-focusing curvature
singularity that can form in the spherical gravitational collapse of a bounded
matter distribution obeying the dominant energy condition. This
characterization is based on the limiting behaviour of the mass function in the
neighbourhood of the singularity. Depending on the rate of growth of the mass
as a function of the area radius R, the singularity may be either covered or
naked. The singularity is naked if this growth rate is slower than R, covered
if it is faster than R, and either naked or covered if the growth rate is same
as R.Comment: 12 pages, Latex, significantly revised version, including change of
title. Revised version to appear in Classical and Quantum Gravit
Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations
The truncation method is a collective name for techniques that arise from
truncating a Laurent series expansion (with leading term) of generic solutions
of nonlinear partial differential equations (PDEs). Despite its utility in
finding Backlund transformations and other remarkable properties of integrable
PDEs, it has not been generally extended to ordinary differential equations
(ODEs). Here we give a new general method that provides such an extension and
show how to apply it to the classical nonlinear ODEs called the Painleve
equations. Our main new idea is to consider mappings that preserve the
locations of a natural subset of the movable poles admitted by the equation. In
this way we are able to recover all known fundamental Backlund transformations
for the equations considered. We are also able to derive Backlund
transformations onto other ODEs in the Painleve classification.Comment: To appear in Nonlinearity (22 pages
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
Multi-frequency scatter broadening evolution of pulsars - I
We present multi-wavelength scatter broadening observations of 47 pulsars,
made with the Giant Metre-wave Radio Telescope (GMRT), Ooty Radio Telescope
(ORT) and Long Wavelength Array (LWA). The GMRT observations have been made in
the phased array mode at 148, 234, and 610 MHz and the ORT observations at 327
MHz. The LWA data sets have been obtained from the LWA pulsar data archive. The
broadening of each pulsar as a function of observing frequency provides the
frequency scaling index, . The estimations of have been
obtained for 39 pulsars, which include entirely new estimates for 31 pulsars.
This study increases the total sample of pulsars available with
estimates by 50\%. The overall distribution of with the
dispersion measure (DM) of pulsar shows interesting variations, which are
consistent with the earlier studies. However, for a given value of DM a range
of values are observed, indicating the characteristic turbulence along
each line of sight. For each pulsar, the estimated level of turbulence,
, has also been compared with and DM. Additionally, we
compare the distribution of with the theoretically predicated model to
infer the general characteristics of the ionized interstellar medium (ISM).
Nearly 65\% of the pulsars show a flatter index (i.e., ) than
that is expected from the Kolmogorov turbulence model. Moreover, the group of
pulsars having flatter index is typically associated with an enhanced value of
than those with steeper index.Comment: 13 pages, 4 figures, 3 tables. Accepted for publication in Ap
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