Related papers: Rigidity aspects of Penrose's singularity theorem

The Penrose strong cosmic censorship conjecture asserts that Cauchy horizons inside dynamically formed black holes are unstable to remnant matter fields that fall into the black holes. The physical importance of this conjecture stems from…

In this note we prove a global rigidity result for asymptotically flat, scalar flat Euclidean hypersurfaces with a minimal horizon lying in a hyperplane, under a natural ellipticity condition. As a consequence we obtain, in the context of…

Transforming Penrose's intuitive picture of a strong cosmic censorship principle, that generically forbids the appearance of locally naked space-time singularities, into a formal mathematical proof, remains at present, one of the most…

This work is an extensive literature review focusing on a few of the important topics in the large-scale structure of spacetime. The work is a Bachelor's thesis submitted at the Institute of Theoretical Physics, University of Leipzig. The…

We review uniqueness theorems as well as other general results about higher dimensional black hole spacetimes. This includes in particular theorems about the topology of higher dimensional spacetimes, theorems about their symmetries…

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,…

A general property of universes without initial singularity is investigated based on the singularity theorem, assuming the null convergence condition and the global hyperbolicity. As a direct consequence of the singularity theorem, the…

Recently, the gravitational collapse of an infinite cylindrical thin shell of matter in an otherwise empty spacetime with two hypersurface orthogonal Killing vectors was studied by Gon\c{c}alves [Phys. Rev. {\bf D65}, 084045 (2002).]. By…

It has previously been shown [W. Rudnicki, Phys. Lett. A 224, 45 (1996)] that a generic gravitational collapse cannot result in a naked singularity accompanied by closed timelike curves. An important role in this result plays the so-called…

The Schwarzschild spacetime metric of negative mass is well-known to contain a naked singularity. In a spacelike slice, this singularity of the metric is characterized by the property that nearby surfaces have arbitrarily small area. We…

We review recent work on the existence and nature of cosmological singularities that can be formed during the evolution of generic as well as specific cosmological spacetimes in general relativity. We first discuss necessary and sufficient…

We prove global hyperbolicity of spacetimes under generic regularity conditions on the metric. We then show that these spacetimes are timelike and null geodesically complete if the gradient of the lapse and the extrinsic curvature $K$ are…

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…

In singularity generating spacetimes both the out-going and in-going expansions of null geodesic congruences $\theta ^{+}$ and $\theta ^{-}$ should become increasingly negative without bound, inside the horizon. This behavior leads to…

In this contribution, we study spacetimes of cosmological interest, without making any symmetry assumptions. We prove a rigid Hawking singularity theorem for positive cosmological constant, which sharpens known results. In particular, it…

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…

We consider spacetimes with compact Cauchy hypersurfaces and with Ricci tensor bounded from below on the set of timelike unit vectors, and prove that the results known for spacetimes satisfying the timelike convergence condition, namely,…

We prove that the Penrose limit of a spacetime along a homogeneous geodesic is a homogeneous plane wave spacetime and that the Penrose limit of a reductive homogeneous spacetime along a homogeneous geodesic is a Cahen--Wallach space. We…

This paper is a further development of the approach to weak cosmic censorship proposed by the authors in Ref. 5. We state and prove a modified version of that work's main result under significantly relaxed assumptions on the asymptotic…

A time-flat condition on spacelike 2-surfaces in spacetime is considered here. This condition is analogous to constant torsion condition for curves in three dimensional space and has been studied in [2, 4, 5, 12, 13]. In particular, any…