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A stable class of spacetimes with naked singularities

Marcus Kriele (1997)

Banach Center Publications

We present a stable class of spacetimes which satisfy the conditions of the singularity theorem of Hawking & Penrose (1970), and which contain naked singularities. This offers counterexamples to a geometric version of the strong cosmic censorship hypothesis.

Critical phenomena in gravitational collapse

Carsten Gundlach (1997)

Banach Center Publications

A mini-introduction to critical phenomena in gravitational collapse is combined with a more detailed discussion of how gravity regularizes the 'critical spacetimes' that dominate these phenomena.

Fastest curves and toroidal black holes

E. Woolgar (1997)

Banach Center Publications

We discuss an apparent paradox (and conjectured resolution) of Jacobson and Venkataramani concerning 'temporarily toroidal' black hole horizons, in light of a recent connectivity theorem for spaces of complete causal curves. We do this in a self-contained manner by first reviewing the 'fastest curve argument' which proves this connectivity theorem, and we note that active topological censorship can be derived as a corollary of this argument. We argue that the apparent paradox arises only when one...

Nature of the central singularity in Szekeres models

Pankaj Joshi, Andrzej Królak (1997)

Banach Center Publications

The occurrence and nature of the central naked singularity in aspherical Szekeres models is investigated here, and the strength of the singularity is discussed. The implications for the cosmic censorship hypothesis are considered.

Special Functions and Pathways for Problems in Astrophysics: An Essay in Honor of A.M. Mathai

Haubold, Hans, Kumar, Dilip, Nair, Seema, Joseph, Dhannya (2010)

Fractional Calculus and Applied Analysis

The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information...

Sur la géométrie de la singularité initiale des espaces-temps plats globalement hyperboliques

Mehdi Belraouti (2014)

Annales de l’institut Fourier

On étudie le comportement asymptotique des niveaux d’une fonction temps quasi-concave, définie sur un espace-temps globalement hyperbolique maximal plat de dimension trois, admettant une hypersurface de Cauchy de genre 2 . On donne une réponse positive à une conjecture posée par Benedetti et Guadagnini dans [7]. Plus précisément, on montre que les niveaux d’une telle fonction temps convergent au sens de la topologie de Hausdorff-Gromov équivariante vers un arbre réel. On montre de plus que la limite...

Weakly regular T 2 -symmetric spacetimes. The global geometry of future Cauchy developments

Philippe LeFloch, Jacques Smulevici (2015)

Journal of the European Mathematical Society

We provide a geometric well-posedness theory for the Einstein equations within the class of weakly regular vacuum spacetimes with T 2 -symmetry, as defined in the present paper, and we investigate their global causal structure. Our assumptions allow us to give a meaning to the Einstein equations under weak regularity as well as to solve the initial value problem under the assumed symmetry. First, introducing a frame adapted to the symmetry and identifying certain cancellation properties taking place...

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