相关论文: Spacetime singularities and curvature blow-ups
In this talk we analyze the effect of recently proposed classes of sudden future singularities on causal geodesics of FLRW spacetimes. Geodesics are shown to be extendible and just the equations for geodesic deviation are singular, although…
Under spherical symmetry, with double-null coordinates $(u,v)$, we study the gravitational collapse of the Einstein--scalar field system with a positive cosmological constant. The spacetime singularities arise when area radius $r$ vanishes…
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.…
Given an extendible spacetime one may ask how much, if any, uniqueness can in general be expected of the extension. Locally, this question was considered and comprehensively answered in a recent paper of Sbierski, where he obtains local…
A hairy extension of the Bertotti-Robinson regular spacetime has been recently introduced in the context of the Einstein-Maxwell-Scaler theory that surprisingly is a singular black hole formed in the $S_{3}$ background spatial topology…
Assuming the Bousso bound, we prove a singularity theorem: if the light rays entering a hyperentropic region contract, then at least one light ray must be incomplete. "Hyperentropic" means that the entropy of the region exceeds the…
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…
The strong cosmic censorship conjecture, introduced by Penrose five decades ago, asserts that, in self-consistent theories of gravity, Cauchy horizons inside dynamically formed black holes should be unstable to remnant perturbation fields…
In this paper we propose a weaker version of Penrose's much heeded Strong Cosmic Censorship (SCC) conjecture, asserting inextentability of maximal Cauchy developments by manifolds with Lipschitz continuous Lorentzian metrics and Riemann…
An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime…
Conjugate points play an important role in the proofs of the singularity theorems of Hawking and Penrose. We examine the relation between singularities and conjugate points in FLRW spacetimes with a singularity. In particular we prove a…
Higher-dimensional braneworld models which contain both bulk and brane curvature terms in the action admit cosmological singularities of rather unusual form and nature. These `quiescent' singularities, which can occur both during the…
In this paper we analyze the effect of recently proposed classes of sudden future singularities on causal geodesics of FLRW spacetimes. Geodesics are shown to be extendible and just the equations for geodesic deviation are singular,…
New general results of non-existence and rigidity of spacelike submanifolds immersed in a spacetime, whose mean curvature is a time-oriented causal vector field, are given. These results hold for a wide class of spacetimes which includes…
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…
The gravitational strength of the central singularity in spherically symmetric space-times is investigated. Necessary conditions for the singularity to be gravitationally weak are derived and it is shown that these are violated in a wide…
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…
We investigate the instability of the Cauchy horizon caused by causality violation in the compact vacuum universe with the topology $B\times {\bf S}^{1}\times {\bf R}$, which Moncrief and Isenberg considered. We show that if the occurrence…
Many central problems in geometry, topology, and mathematical physics lead to questions concerning the long-time dynamics of solutions to ordinary and partial differential equations. Examples range from the Einstein field equations of…
This paper studies the singularity structure of FLRW spacetimes without particle horizons at the $C^0$-level of the metric. We show that in the case of constant spatial curvature $K=+1$, and without any further assumptions on the scale…