Related papers: Volume Singularities in General Relativity
It is shown that the initial singularities in spatially compact spacetimes with spherical, plane or hyperbolic symmetry admitting a compact constant mean curvature hypersurface are crushing singularities when the matter content of spacetime…
In General Relativity, gravity is universally attractive, a feature embodied by the Raychaudhuri equation which requires that the expansion of a congruence of geodesics is always non-increasing, as long as matter obeys the strong or weak…
Spacetime singularities in general relativity are commonly thought to be problematic, in that they signal a breakdown in the theory. We address the question of how to interpret this breakdown, restricting our attention to classical…
General Relativity simplifies dramatically in the limit that the number of spacetime dimensions D is infinite: it reduces to a theory of non-interacting particles, of finite radius but vanishingly small cross sections, which do not emit nor…
We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic,…
An overview is provided of the singularity theorems in cosmological contexts at a level suitable for advanced graduate students. The necessary background from tensor and causal geometry to understand the theorems is supplied, the…
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…
New Planck scale physics may solve the singularity problems of classical general relativity and may lead to interesting consequences for very early Universe cosmology. Two approaches to these questions are reviewed in this article. The…
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,…
Black holes are probably among the most fascinating objects populating our universe. Their characteristic features found within general relativity, encompassing spacetime singularities, event horizons, and black hole thermodynamics, provide…
Gravitational collapse of radiation shells in a non self-similar higher dimensional spherically symmetric spacetime is studied. Strong curvature naked singularities form for a highly inhomogeneous collapse, violating the cosmic censorship…
I review elements of the foundations of black-hole theory with attention to problematic issues, and describe some techniques which either seem to help with the difficulties or at least investigate their scope. The definition of black holes…
We prove a singularity theorem in semiclassical gravity without assuming global hyperbolicity or the null energy/curvature condition; the former is replaced by the weaker causality conditions of stable causality and past reflectivity, and…
Spherically symmetric space-times provide many examples for interesting black hole solutions, which classically are all singular. Following a general program, space-like singularities in spherically symmetric quantum geometry, as well as…
We summarize the main ideas of General Relativity and Lorentzian geometry, leading to a proof of the simplest of the celebrated Hawking-Penrose singularity theorems. The reader is assumed to be familiar with Riemannian geometry and point…
We show that the absence of unbounded algebraic curvature invariants constructed from polynomials of the Riemann tensor cannot guarantee the absence of strong singularities. As a consequence, it is not sufficient to rely solely on the…
Black holes are an apparently unavoidable prediction of classical General Relativity, at least if matter obeys the strong energy condition rho + 3p > 0. However quantum vacuum fluctuations generally violate this condition, as does the eq.…
We consider singularity theorems in asymptotically anti-de Sitter (AdS) spacetimes. In the first part, we discuss the global methods used to show geodesic incompleteness and see that when the conditions imposed in Hawking and Penrose's…
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…
In this paper, the null geodesics and gravitational lensing in a nonsingular spacetime are investigated. According to the nature of the null geodesics, the spacetime is divided into several cases. In the weak deflection limit, we find the…