The Structure of Singularity in Gravitational Collapse

It has been claimed that the Lemaitre-Tolman-Bondi-de Sitter solution always admits future-pointing radial time-like geodesics emerging from the shell-focussing singularity, regardless of the nature of the (regular) initial data. This is despite the fact that some data rule out the emergence of future pointing radial null geodesics. We correct this claim and show that in general in spherical symmetry, the absence of radial null geodesics emerging from a central singularity is...

Possibilities emerging out of the dynamical evolutions of collapsing systems are addressed in this thesis through analytical investigations of the highly non-linear Einstein Field Equations. Studies of exact solutions and their properties, play a non-trivial role in general relativity, even in the current context. Finding non-trivial solutions to the Einstein field equations requires some reduction of the problem, which usually is done by exploiting symmetries or other proper...

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 usi...

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...

We present here an overview of our basic understanding and recent developments on spacetime singularities in the Einstein theory of gravity. Several issues related to physical significance and implications of singularities are discussed. The nature and existence of singularities are considered which indicate the formation of super ultra-dense regions in the universe as predicted by the general theory of relativity. Such singularities develop during the gravitational collapse ...

The present work investigates the gravitational collapse of a perfect fluid in $f(R)$ gravity models. For a general $f(R)$ theory, it is shown analytically that a collapse is quite possible. The singularity formed as a result of the collapse is found to be a curvature singularity of shell focusing type. The possibility of the formation of an apparent horizon hiding the central singularity depends on the initial conditions.

We study the curvature strength and visibility of the central singularity arising in Tolman-Bondi-de Sitter collapse. We find that the singularity is visible and Tipler strong along an infinite number of timelike geodesics, independently of the initial data, and thus stable against perturbations of the latter.

We comment here on the results in Ref [4] that showed naked singularities in dynamical gravitational collapse of inhomogeneous dust to be stable but non-generic. The definition of genericity used there is reconsidered. We point out that genericity in terms of an open set, with a positive measure defined suitably on the space of initial data, is physically more appropriate compared to the dynamical systems theory definition used in [4] which makes both black holes and naked si...

By considering families of radial null geodesics, we study the subsets of initial data that lead to naked singularities and black holes in inhomogeneous spherical dust collapse. We introduce the notion of central homogeneity for spherical dust collapse and prove that for the occurrence of naked singularities, the initial data set must in general be centrally homogeneous. Even though mathematically this indicates that naked singularities are in general unstable, we show that c...

Formulating a dust filled spherically symmetric metric utilizing the 3+1 formalism for general relativity, we show that the metric coefficients are completely determined by the matter distribution throughout the spacetime. Furthermore, the metric describes both inhomogeneous dust regions and also vacuum regions in a single coordinate patch, thus alleviating the need for complicated matching schemes at the interfaces. In this way, the system is established as an initial-bounda...