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Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which,…
Basis and limitations of singularity theorems for Gravity are examined. As singularity is a critical situation in course of time, study of time paths, in full generality of Equivalence principle, provides two mechanisms to prevent…
In general relativity, gravitational collapse of matter fields ends with the formation of a spacetime singularity, where the matter density becomes infinite and standard physics breaks down. According to the weak cosmic censorship…
Plane symmetric self-similar solutions to Einstein's four-dimensional theory of gravity are studied and all such solutions are given analytically in closed form. The local and global properties of these solutions are investigated and it is…
In a previous paper, we studied the interior solution of a collapsing body in a non-local theory of gravity super-renormalizable at the quantum level. We found that the classical singularity is replaced by a bounce, after which the body…
It is known now that a typical gravitational collapse in general relativity, evolving from regular initial data and under physically reasonable conditions would end in either a black hole or a naked singularity final state. An important…
We study here the gravitational collapse of a matter cloud with a non-vanishing tangential pressure in the presence of a non-zero cosmological term. Conditions for bounce and singularity formation are derived for the model. It is also shown…
An extension of Penrose's singularity theorem is proved for spacetimes where black holes are allowed to form from non-singular initial data. With standard assumptions about the spacetime, and assuming the existence of a trapped surface…
In the presence of a minimal length physical objects cannot collapse to an infinite density, singular, matter point. In this note we consider the possible final stage of the gravitational collapse of "thick" matter layers. The energy…
In this note a time dependent spacetime is explored in the background of $f(R,T)$ gravity via the gravitational collapse of a massive star. The star is modelled by the Vaidya spacetime which is time dependent in nature. The coupling of…
The existence of spacetime singularities is one of the biggest problems of nowadays physics. According to Penrose, each physical singularity should be covered by a "cosmic censor" which prevents any external observer from perceiving their…
We study spherically symmetric static spacetimes generally filled with an anisotropic fluid in the nonrelativistic general covariant theory of gravity. In particular, we find that the vacuum solutions are not unique, and can be expressed in…
One or two negative mass singularities are found to occur in static inhomogeneous spatially closed solutions to the Einstein equations. The singularities produce a positive Komar mass, and this decreases the size of the cosmological…
Through an illuminating thought experiment we demonstrate that the nonsingular "continued collapse" picture of a black hole is the only consistent and physical one. We provide a class exact solutions on the boundary of the space of physical…
In this paper, we consider the gravitational collapse of generalized Vaidya space-time when the matter satisfies the equation of the state either $P=0$ or $P=-\alpha \rho$, where $0 < \alpha < 1$. We show that in the case when type I of…
A massive compact object is that which forms when a sufficiently massive star collapses. This is commonly taken to be a black hole with a singularity surrounded by a horizon and which evolves by emitting Hawking radiation. In a quantum…
A star of mass greater than a critical mass is believed to undergo gravitational collapse to form a singularity, owing to Hawking-Penrose singularity theorem which is based on the Raychaudhuri equation in the absence of torsion. We argue…
The weak cosmic censorship conjecture asserts that spacetime singularities that arise in gravitational collapse are always hidden inside of black holes, invisible to distant observers. This conjecture, put forward by Penrose more than four…
The critical collapse of a scalar field is a threshold solution of black hole formation, in which a naked singularity arises. We study here the curvature strength of this singularity using a numerical ansatz. The behavior of the Jacobi…
We review the status of the weak cosmic censorship conjecture, which asserts, in essence, that all singularities of gravitational collapse are hidden within black holes. Although little progress has been made toward a general proof (or…