Related papers: Conformal transformations near Naked Singularities…
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…
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…
A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the…
It was recently shown that the metric functions which describe a spherically symmetric space-time with vanishing radial pressure can be explicitly integrated. We investigate the nakedness and curvature strength of the shell-focusing…
We discuss an alternative approach to the uniformisation problem on surfaces with boundary by representing conformal structures on surfaces $M$ of general type by hyperbolic metrics with boundary curves of constant positive geodesic…
We study the collapse of a spherically symmetric dust distribution in $d$-dimensional AdS spacetime. We investigate the role of dimensionality, and the presence of a negative cosmological constant, in determining the formation of trapped…
The causal character of singularities is often studied in relation to the existence of naked singularities and the subsequent possible violation of the cosmic censorship conjecture. Generally one constructs a model in the framework of…
One of the fundamental unanswered questions in the general theory of relativity is whether ``naked'' singularities, that is singular events which are visible from infinity, may form with positive probability in the process of gravitational…
We investigate here spherically symmetric gravitational collapse in a spacetime with an arbitrary number of dimensions and with a general {\it type I} matter field, which is a broad class that includes most of the physically reasonable…
The collapse of marginally bound, inhomogeneous, pressureless (dust) matter, in spherical symmetry, is considered. The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions.…
In the present work we study spherically symmetric gravitational collapse of a homogeneous perfect fluid in the context of Generalized Rastall Theory (GRT). In this modified version of the original {Rastall Gravity (RG)}, the coupling…
We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal transformation.
Gravitational collapse is one of the most striking phenomena in gravitational physics. The cosmic censorship conjecture has provided strong motivation for researches in this field. In the absence of general proof for the censorship, many…
We numerically investigate the gravitational collapse of collisionless particles in spheroidal configurations both in four and five-dimensional (5D) space-time. We repeat the simulation performed by Shapiro and Teukolsky (1991) that…
Gravitational collapse singularities are undesirable, yet inevitable to a large extent in General Relativity. When matter satisfying null energy condition collapses to the extent a closed trapped surface is formed, a singularity is…
We discuss a notion of discrete conformal equivalence for decorated piecewise euclidean surfaces (PE-surface), that is, PE-surfaces with a choice of circle about each vertex. It is closely related to inversive distance and hyperideal circle…
The conformal geometry of surfaces in the conformal space $\mathbf Q^n_1$ is studied. We classify the space-like surfaces in $\mathbf Q^n_1$ with vanishing conformal form up to conformal equivalence.
The null curvature condition (NCC) is the requirement that the Ricci curvature of a Lorentzian manifold be nonnegative along null directions, which ensures the focusing of null geodesic congruences. In this note, we show that the NCC…
We consider spherically symmetric spacetimes with matter whose timelike flow is assumed to be shear-free. A number of results on the formation and visibility of spacetime singularities is proven, with the main one being that shear-free…
We analyse here the gravitational collapse of directed null radiation in a background with a constant potential such as one produced by a star system like galaxy in which the collapsing object is immersed. Both naked singularities and black…