Related papers: Mathematical General Relativity
For almost half of the one hundred year history of Einstein's theory of general relativity, Strong Cosmic Censorship has been one of its most intriguing conjectures. The SCC conjecture addresses the issue of the nature of the singularities…
We give ansatze for solving classically the initial value constraints of general relativity minimally coupled to a scalar field, electromagnetism or Yang-Mills theory. The results include both time-symmetric and asymmetric data. The…
We discuss several aspects of cosmic censorship hypothesis. There is evidence both in favor and against the hypothesis. On one hand one can prove that cosmic censorship holds in several special cases and on the other hand there is a number…
The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of 'Cauchy hypersurfaces': (1) structure of globally hyperbolic…
Spacetime singularities that arise in gravitational collapse are always hidden inside of black holes. This is the essence of the weak cosmic censorship conjecture. The hypothesis, put forward by Penrose 40 years ago, is still one of the…
The cosmic censorship hypothesis, introduced by Penrose forty years ago, is one of the corner stones of general relativity. This conjecture asserts that spacetime singularities that arise in gravitational collapse are always hidden inside…
The 1965 Penrose singularity theorem demonstrates the utterly inevitable and unavoidable formation of spacetime singularities under physically reasonable assumptions, and it remains one of the main results in our understanding of black…
We present here a spectrum of developments and predictions in gravitation theory in recent years which appear to be amongst some of the most exciting directions. These include the spacetime singularities, gravitational collapse final…
Cosmic censorship posits spacetime singularities remain concealed behind event horizons, preserving the determinism of General Relativity. While quantum gravity is expected to resolve singularities, we argue that cosmic censorship remains…
We review selected recent results concerning the global structure of solutions of the vacuum Einstein equations. The topics covered include quasi-local mass, strong cosmic censorship, non-linear stability, new constructions of solutions of…
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…
Motivated by the endeavors of Li Xiang and You-Gen Shen on naked singularities, we investigate the validity of the cosmic censorship conjecture in the context of generalized uncertainty principle. In particular, upon considering both linear…
According to the cosmic censorship hypothesis of Penrose, naked singularities should never occur in realistic collapse situations. One of the major open problems in this context is the existence of a naked singularity in the Kerr solution…
End state of gravitational collapse and the related cosmic censorship conjecture continue to be amongst the most important open problems in gravitation physics today. My purpose here is to bring out several aspects related to gravitational…
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.…
Cosmic censorship is known to fail in some well-controlled phenomena, calling into question the predictive power of General Relativity and opening up the possibility of observing Planck-scale physics. We propose that the cosmic censorship…
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…
The Averaging problem in general relativity and cosmology is discussed. The approach of macroscopic gravity to resolve the problem is presented. An exact cosmological solution to the equations of macroscopic gravity is given and its…
In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by an initial Cauchy data, it suggests a creation of a naked singularity, thus…
Strong cosmic censorship holds that given suitable initial data on a spacelike hypersurface, the laws of general relativity should determine, completely and uniquely, the future evolution of the spacetime. Here it is argued that while…