A geodesically complete space-time with a crushing null hypersurface

In this paper, we study rigidity aspects of Penrose's singularity theorem. Specifically, we aim to answer the following question: if a spacetime satisfies the hypotheses of Penrose's singularity theorem except with weakly trapped surfaces instead of trapped surfaces, then what can be said about the global spacetime structure if the spacetime is null geodesically complete? In this setting, we show that we obtain a foliation of MOTS which generate totally geodesic null hypersur...

This paper has been withdrawn by the author due to the triviality of the considered coordinate transformations. A consistent treatment, based on the extended physical radial coordinates, is presented in the publications of the author 2000 - 2003.

This paper was withdrawn by the author.

It has been suggested by Israel that the Kerr singularity cannot be strong in the sense of Tipler, for it tends to cause repulsive effects. We show here that, contrary to that suggestion, nearly all null geodesics reaching this singularity do in fact terminate in Tipler's strong curvature singularity. Implications of this result are discussed in the context of an earlier cosmic censorship theorem which constraints the occurrence of Kerr-like naked singularities in generic col...

This paper explains why spacetime singularities do not constitute a breakdown of physical laws, and points out that the difference between the metrics at singularities and those outside of singularities is factual, rather than nomological.

I discuss singular spacetimes in the context of the geometrized formulation of Newtonian gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian gravitation is singular, and then I show that singularities in this sense arise naturally in classical physics by stating and proving a classical version of the Raychaudhuri-Komar singularity theorem.

This paper compares recent approaches appearing in the literature on the singularity problem for space-times with nonvanishing torsion.

It is widely expected that generic black holes have a non-empty but weakly singular Cauchy horizon, due to mass inflation. Indeed this has been proven by the author in the spherical collapse of a charged scalar field, under decay assumptions of the field in the black exterior which are conjectured to be generic. A natural question then arises: can this weakly singular Cauchy horizon close off the space-time, or does the weak null singularity necessarily "break down", giving w...

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 conditions for the existence of geodesically incomplete spacetimes based on a tensorial analysis of the geodesic equations. We then classify the possible singularities of isotropic globally hyperbolic universes using the Bel-Robinson slice ...

A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of singular null geodesics to existence of regular curves which are super-solutions of the radial null geodesic equation, and allows us to treat all the known examples of naked singularities from a unified viewpoint. New examples are also found usi...