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 $p=k\rho$. 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

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

On the Role of Initial Data in the Gravitational Collapse of Inhomogeneous Dust

We consider here the gravitational collapse of a spherically symmetric inhomogeneous dust cloud described by the Tolman-Bondi models. By studying a general class of these models, we find that the end state of the collapse is either a black hole or a naked singularity, depending on the parameters of the initial density distribution, which are $\rho_{c}$, the initial central density of the massive body, and $R_0$, the initial boundary. The collapse ends in a black hole if the dimensionless quantity $\beta$ constructed out of this initial data is greater than 0.0113, and it ends in a naked singularity if $\beta$ is less than this number. A simple interpretation of this result can be given in terms of the strength of the gravitational potential at the starting epoch of the collapse.Comment: Original title changed, numerical range of naked singularity corrected. Plain Tex File. 14 pages. To appear in Physical Review

The study of gravitational collapse model in higher dimensional space-time

We investigate the end state of the gravitational collapse of an inhomogeneous dust cloud in higher dimensional space-time. The naked singularities are shown to be developing as the final outcome of non-marginally bound collapse. The naked singularities are found to be gravitationally strong in the sense of Tipler .Comment: 6 Latex pages, No figure, Revtex styl

On naked singularities in higher dimensional Vaidya space-times

We investigate the end state of gravitational collapse of null fluid in higher dimensional space-times. Both naked singularities and black holes are shown to be developing as final outcome of the collapse. The naked singularity spectrum in collapsing Vaidya region (4D) gets covered with increase in dimensions and hence higher dimensions favor black hole in comparison to naked singularity. The Cosmic Censorship Conjecture will be fully respected for a space of infinite dimension.Comment: 9 pages, LateX, Minor changes. Accepted in Phys. Rev.

Incidence of HI 21-cm absorption in strong FeII systems at 0.5<z<1.50.5<z<1.5

We present the results from our search for HI 21-cm absorption in a sample of 16 strong FeII systems ($W_{\rm r}$(MgII $\lambda2796$) $\ge1.0$ \AA\ and $W_{\rm r}$(FeII $\lambda2600$) or $W_{\rm FeII}$ $\ge1$ \AA) at $0.5<z<1.5$ using the Giant Metrewave Radio Telescope and the Green Bank Telescope. We report six new HI 21-cm absorption detections from our sample, which have increased the known number of detections in strong MgII systems at this redshift range by $\sim50$%. Combining our measurements with those in the literature, we find that the detection rate of HI 21-cm absorption increases with $W_{\rm FeII}$, being four times higher in systems with $W_{\rm FeII}$ $\ge1$ \AA\ compared to systems with $W_{\rm FeII}$ $<1$ \AA. The $N$(HI) associated with the HI 21-cm absorbers would be $\ge 2 \times 10^{20}$ cm$^{-2}$, assuming a spin temperature of $\sim500$ K (based on HI 21-cm absorption measurements of damped Lyman-$\alpha$ systems at this redshift range) and unit covering factor. We find that HI 21-cm absorption arises on an average in systems with stronger metal absorption. We also find that quasars with HI 21-cm absorption detected towards them have systematically higher $E(B-V)$ values than those which do not. Further, by comparing the velocity widths of HI 21-cm absorption lines detected in absorption- and galaxy-selected samples, we find that they show an increasing trend (significant at $3.8\sigma$) with redshift at $z<3.5$, which could imply that the absorption originates from more massive galaxy haloes at high-$z$. Increasing the number of HI 21-cm absorption detections at these redshifts is important to confirm various trends noted here with higher statistical significance.Comment: 17 pages, 10 figures, 8 tables, accepted for publication in MNRA

Naked Singularities in Spherically Symmetric Inhomogeneous Tolman-Bondi Dust Cloud Collapse

We investigate the occurrence and nature of naked singularity for the inhomogeneous gravitational collapse of Tolman-Bondi dust clouds.It is shown that the naked singularities form at the center of the collapsing cloud in a wide class of collapse models which includes the earlier cases considered by Eardley and Smarr and Christodoulou. This class also contains self-similar as well as non-self-similar models. The structure and strength of this singularity is examined and the question is investigated as to when a non-zero measure set of non-spacelike trajectories could be emitted from the singularity as opposed to isolated trajectories coming out. It is seen that the weak energy condition and positivity of energy density ensures that the families of non-spacelike trajectories come out of the singularity. The curvature strength of the naked singularity is examined which provides an important test for its physical significance and powerful curvature growth near the naked singularity is pointed out for several subclasses considered. The conditions are discussed for the naked singularity to be globally naked. Implications for the basic issue of the final fate of gravitational collapse are considered once the inhomogeneities in the matter distribution are taken into account. It is argued that a physical formulation for the cosmic censorship may be evolved which avoids the features above. Possibilities in this direction are discussed while indicating that the analysis presented here should be useful for any possible rigorous formulation of the cosmic censorship hypothesis.Comment: 41 pages, TIFR preprint TAP 9/9

North-South Distribution of Solar Flares during Cycle 23

In this paper, we investigate the spatial distribution of solar flares in the northern and southern hemisphere of the Sun that occurred during the period 1996 to 2003. This period of investigation includes the ascending phase, the maximum and part of descending phase of solar cycle 23. It is revealed that the flare activity during this cycle is low compared to previous solar cycle, indicating the violation of Gnevyshev-Ohl rule. The distribution of flares with respect to heliographic latitudes shows a significant asymmetry between northern and southern hemisphere which is maximum during the minimum phase of the solar cycle. The present study indicates that the activity dominates the northern hemisphere in general during the rising phase of the cycle (1997-2000). The dominance of northern hemisphere is shifted towards the southern hemisphere after the solar maximum in 2000 and remained there in the successive years. Although the annual variations in the asymmetry time series during cycle 23 are quite different from cycle 22, they are comparable to cycle 21.Comment: 6 pages, 2 figures, 1 table; Accepted for the publication in the proceedings of international solar workshop held at ARIES, Nainital, India on "Transient Phenomena on the Sun and Interplanetary Medium" in a special issue of "Journal of Astrophysics and Astronomy (JAA)