Pankaj S. Joshi

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.

Gravitational Collapse and Spacetime Singularities

Physical phenomena in astrophysics and cosmology involve gravitational collapse in a fundamental way. The final fate of a massive star when it collapses under its own gravity at the end of its life cycle is one of the most important questions in gravitation theory and relativistic astrophysics, and is the foundation of blackhole physics. General relativity predicts that continual gravitational collapse gives rise to a spacetime singularity, which may be hidden inside an event horizon or visible to external observers. This book investigates these issues, and shows how such visible ultra-dense regions arise naturally and generically as an outcome of dynamical gravitational collapse. Quantum gravity may take over in these regimes to resolve the classical spacetime singularity. The quantum effects from a visible extreme gravity region could then propagate to external observers, providing a useful laboratory for quantum gravity, and implying interesting consequences for ultra-high energy astrophysical phenomena in the universe. This volume will be of interest to graduate students and academic researchers in gravitation physics and fundamental physics, as well as in astrophysics and cosmology. It includes a review of recent research into gravitational collapse, and several examples of collapse models are worked out in detail.

Why do naked singularities form in gravitational collapse? II

We investigate what are the key physical features that cause the development of a naked singularity, rather than a black hole, as the end-state of spherical gravitational collapse. We show that sufficiently strong shearing effects near the singularity delay the formation of the apparent horizon. This exposes the singularity to an external observer, in contrast to a black hole, which is hidden behind an event horizon due to the early formation of an apparent horizon.

Recent developments in gravitational collapse and spacetime singularities

It is now known that when a massive star collapses under the force of its own gravity, the final fate of such a continual gravitational collapse will be either a black hole or a naked singularity under a wide variety of physically reasonable circumstances within the framework of general theory of relativity. The research of recent years has provided considerable clarity and insight on stellar collapse, black holes and the nature and structure of spacetime singularities. We discuss several of these developments here. There are also important fundamental questions that remain unanswered on the final fate of collapse of a massive matter cloud in gravitation theory, especially on naked singularities which are hypothetical astrophysical objects and on the nature of cosmic censorship hypothesis. These issues have key implications for our understanding on black hole physics today, its astrophysical applications, and for certain basic questions in cosmology and possible quantum theories of gravity. We consider these issues here and summarize recent results and current progress in these directions. The emerging astrophysical and observational perspectives and implications are discussed, with particular reference to the properties of accretion disks around black holes and naked singularities, which may provide characteristic signatures and could help distinguish these objects.

Gravitational Collapse: The Story So Far

An outstanding problem in gravitation theory and relativistic astrophysics today is to understand the final outcome of an endless gravitational collapse. Such a continual collapse would take place when stars more massive than few times the mass of the sun collapse under their own gravity on exhausting their nuclear fuel. According to the general theory of relativity, this results either in a black hole, or a naked singularity — which can communicate with far away observers in the universe. While black holes are (almost) being detected and are increasingly used to model high energy astrophysical phenomena, naked singularities have turned into a topic of active discussion, aimed at understanding their structure and implications. Recent developments here are reviewed, indicating future directions.

Distinguishing black holes from naked singularities through their accretion disc properties

We show that, in principle, a slowly evolving gravitationally collapsing perfect fluid cloud can asymptotically settle to a static spherically symmetric equilibrium configuration with a naked singularity at the center. We consider one such asymptotic final configuration with a finite outer radius, and construct a toy model in which it is matched to a Schwarzschild exterior geometry. We examine the properties of circular orbits in this model. We then investigate the observational signatures of a thermal accretion disc in this spacetime, comparing them with the signatures expected for a disc around a black hole of the same mass. Several notable differences emerge. A disc around the naked singularity is much more luminous than one around an equivalent black hole. Also, the disc around the naked singularity has a spectrum with a high frequency power law segment that carries a major fraction of the total luminosity. Thus, at least some naked singularities can, in principle, be distinguished observationally from the black holes of the same mass. We discuss the possible implications of these results.

Initial data and the end state of spherically symmetric gravitational collapse

Generalizing earlier results on the initial data and the final fate of dust collapse, we study here the relevance of the initial state of a spherically symmetric matter cloud towards determining its end state in the course of a continuing gravitational collapse. It is shown that given an arbitrary regular distribution of matter at the initial epoch, there always exists an evolution from this initial data which would result either in a black hole or a naked singularity, depending on the allowed choice of free functions available in the solution. It follows that given any initial density and pressure profiles for the cloud, there is a non-zero measure set of configurations leading either to black holes or naked singularities, subject to the usual energy conditions ensuring the positivity of energy density. We also characterize here wide new families of black hole solutions resulting from spherically symmetric collapse without requiring the cosmic censorship assumption.

Kerr Naked Singularities as Particle Accelerators

We investigate here the particle acceleration by Kerr naked singularities. We consider a collision between particles dropped in from infinity at rest, which follow geodesic motion in the equatorial plane, with their angular momenta in an appropriate finite range of values. When an event horizon is absent, an initially infalling particle turns back as an outgoing particle, when it has the angular momentum in an appropriate range of values, which then collides with infalling particles. When the collision takes place close to what would have been the event horizon in the extremal case, the center-of-mass energy of the collision is arbitrarily large, depending on how close the overspinning Kerr geometry is to the extremal case. Thus, the fast rotating Kerr configurations if they exist in nature could provide an excellent cosmic laboratory to probe ultrahigh-energy physics.

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

Gravitational collapse and the cosmological constant

\rho_{c}