arXiv subjects

T. P. Singh

Publications and source records attributed to T. P. Singh.

67 records · Page 4Linked to original sources

arXiv1998

Gravitational Collapse, Black Holes and Naked Singularities

This article gives an elementary review of gravitational collapse and the cosmic censorship hypothesis. Known models of collapse resulting in the formation of black holes and naked singularities are summarized. These models, when taken together, suggest that the censorship hypothesis may not hold in classical general relativity. The nature of the quantum processes that take place near a naked singularity, and their possible implication for observations, is briefly discussed.

gr-qc↗

arXiv1998

Gamma-Ray Bursts and Quantum Cosmic Censorship

Gamma-ray bursts are believed to result from the coalescence of binary neutron stars. However, the standard proposals for conversion of the gravitational energy to thermal energy have difficulties. We show that if the merger of the two neutron stars results in a naked singularity, instead of a black hole, the ensuing quantum particle creation can provide the requisite thermal energy in a straightforward way. The back-reaction of the created particles can avoid the formation of the naked singularity predicted by the classical theory. Hence cosmic censorship holds in the quantum theory, even if it were to be violated in classical general relativity.

gr-qc↗

arXiv1997

Null Geodesic Expansion in Spherical Gravitational Collapse

We derive an expression for the expansion of outgoing null geodesics in spherical dust collapse and compute the limiting value of the expansion in the approach to singularity formation. An analogous expression is derived for the spherical collapse of a general form of matter. We argue on the basis of these results that the covered as well as the naked singularity solutions arising in spherical dust collapse are stable under small changes in the equation of state.

gr-qc↗

arXiv1997

Naked singularities and the Weyl Curvature Hypothesis

We examine the growth of the Weyl curvature in two examples of naked singularity formation in spherical gravitational collapse - dust and the Vaidya spacetime. We find that the Weyl scalar diverges along outgoing radial null geodesics as they meet the naked singularity in the past. The implications of this result for the Weyl curvature hypothesis are discussed. We mention the possibility that although classical general relativity admits naked singularity solutions arising from gravitational collapse, the second law of thermodynamics could forbid their occurrence in nature. The method can also be used to compare the relative importance of initial data and that of the energy-momentum tensor in deciding the metric solution in any general case.

gr-qc↗

arXiv1997

Are naked singularites forbidden by the second law of thermodynamics?

By now, many examples of naked singularities in classical general relativity are known. It may however be that a physical principle over and above the general theory prevents the occurrence of such singularities in nature. Assuming the validity of the Weyl curvature hypothesis, we propose that naked singularities are forbidden by the second law of thermodynamics.

gr-qc↗

arXiv1997

Some comments on the nature of initial data in spherical collapse

Various authors have shown the occurence of naked singularities and black holes in the spherical gravitational collapse of inhomogeneous dust. In a recent preprint, Antia has criticised a statement in a paper by Jhingan, Joshi and Singh on dust collapse. We show that his criticism is invalid. Antia shows that in Eulerian coordinates a series expansion for the density of a collapsing Newtonian fluid can have only even powers. However, he has overlooked the fact that Jhingan et al. have actually used Lagrangian (comoving) coordinates, and not Eulerian coordinates. As we show, in Lagrangian coordinates there is no restriction that the density have only even powers and hence his criticism is invalid. We also point out that an earlier claim by Antia on the instability of strong naked singularities in dust collapse is not supported by any concrete analysis, and is hence incorrect.

gr-qc↗

arXiv1997

Cosmic censorship and spherical gravitational collapse with tangential pressure

We study the spherical gravitational collapse of a compact object under the approximation that the radial pressure is identically zero, and the tangential pressure is related to the density by a linear equation of state. It turns out that the Einstein equations can be reduced to the solution of an integral for the evolution of the area radius. We show that for positive pressure there is a finite region near the center which necessarily expands outwards, if collapse begins from rest. This region could be surrounded by an inward moving one which could collapse to a singularity - any such singularity will necessarily be covered by a horizon. For negative pressure the entire object collapses inwards, but any singularities that could arise are not naked. Thus the nature of the evolution is very different from that of dust, even when the ratio of pressure to density is infinitesimally small.

gr-qc↗

arXiv1996

Negative Pressure and Naked Singularities in Spherical Gravitational Collapse

Assuming the weak energy condition, we study the nature of the non-central shell-focussing singularity which can form in the gravitational collapse of a spherical compact object in classical general relativity. We show that if the radial pressure is positive, the singularity is covered by a horizon. For negative radial pressures, the singularity will be covered if the ratio of pressure to the density is greater than -1/3 and naked if this ratio is $\leq -1/3$.

gr-qc↗

arXiv1996

The final fate of spherical inhomogeneous dust collapse II: Initial data and causal structure of singularity

Further to results in [9], pointing out the role of initial density and velocity distributions towards determining the final outcome of spherical dust collapse, the causal structure of singularity is examined here in terms of evolution of the apparent horizon. We also bring out several related features which throw some useful light towards understanding the nature of this singularity, including the behaviour of geodesic families coming out and some aspects related to the stability of singularity.

gr-qc↗

arXiv1996

Gravitational Collapse and Cosmic Censorship

This article gives an elementary overview of the end-state of gravitational collapse according to classical general relativity. The focus of discussion is the formation of black holes and naked singularities in various physically reasonable models of gravitational collapse. Possible implications for the cosmic censorship hypothesis are outlined.

gr-qc↗

arXiv1995

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 $ρ_{c}$, 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 $β$ constructed out of this initial data is greater than 0.0113, and it ends in a naked singularity if $β$ 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.

gr-qc↗

arXiv1994

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.

gr-qc↗

arXiv1993

The Quasi-Linear Evolution of the Density Field in Models of Gravitational Instability

Two quasi-linear approximations, the frozen flow approximation (FFA) and the frozen potential approximation (FPA), have been proposed recently for studying the evolution of a collisionless self-gravitating fluid. In the FFA it is assumed that the velocity field remains unchanged from its value obtained from the linear theory whereas in FPA the same approximation is made for the gravitational potential. In this paper we compare these and the older Zel'dovich approximation by calculating the evolution of the density in perturbation theory. In particular we compute the skewness, including the smoothing effects, and the kurtosis for the FFA, FPA and Zel'dovich approximation and compare their relative accuracy.

astro-ph↗