Related papers: Light Rays, Singularities, and All That
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 singularity theorems of classical general relativity are briefly reviewed. The extent to which their conclusions might still apply when quantum theory is taken into account is discussed. There are two distinct quantum loopholes: quantum…
In this review, we provide a concrete overview of the Raychaudhuri equation, Focusing theorem and Convergence conditions in a plethora of backgrounds and discuss the consequences. We also present various classical and quantum approaches…
The prospect of detecting/constraining deviations from general relativity by studying gravitational waves (GWs) from merging black holes has been one of the primary motivations of GW interferometers like LIGO/Virgo. Within pure gravity, the…
This talk describes some recent results [16] regarding the problem of uniqueness in the large (also known as strong cosmic censorship) for the initial value problem in general relativity. In order to isolate the essential analytic features…
These lecture notes are intended as a guide to Graduate level readers that are already familiar with basic General Relativity. They present in a concise way some advanced concepts and problems encountered in the study of gravitation. In…
The goal of this lecture is to introduce the student to the theory of Special Relativity. Not to overload the content with mathematics, the author will stick to the simplest cases; in particular only reference frames using Cartesian…
After a brief summary of the foundations of general relativity, we will concentrate on the stationary exact solutions of the Einstein and Einstein-Maxwell equations. A number of these solutions can be interpreted as black holes,…
In this short note, a brief overview with a critical appraisal of the acclaimed singularity theorems, the most genuine post-Einsteinian result of General Relativity, is presented.
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…
For the celebrations of the 100 years of the observations undertaken by Eddington at the island of Principe and collaborators at Sobral during a total solar eclipse in May 29, 1919, which have confirmed Einstein's theory of general…
This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of…
In this work we have studied the singular behaviour of gravitational theories with non symmetric connections. For this purpose we introduce a new criteria for the appearance of singularities based on the existence of black/white hole…
Present knowledge about the nature of spacetime singularities in the context of classical general relativity is surveyed. The status of the BKL picture of cosmological singularities and its relevance to the cosmic censorship hypothesis are…
Einstein's genius and penetrating physical intuition led to the general theory of relativity, which incorporates gravity into the geometry of spacetime. However, the theory of general relativity leads to perspectives which go far beyond the…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
We derive causality constraints on the simplest scalar-tensor theories in which black holes differ from what General Relativity predicts, a scalar coupled to the Gauss-Bonnet or the Chern-Simons terms. Demanding that time advances are…
Black holes have often provided profound insights into the nature of gravity and the structure of space-time. The study of the mathematical properties of black objects is a major research theme of contemporary theoretical physics. This…
We show that singularities necessarily occur when a boundary of causality violating set exists in a space-time under the physically suitable assumptions except the global causality condition in the Hawking-Penrose singularity theorems.…
These notes give a concise introduction to General Relativity at the advanced undergraduate level, starting from the weak field limit and gravitational waves, then introducing curved manifolds and Riemannian geometry. The nonlinear…