Related papers: On Singularity Free Spacetimes--II : mid Geodesic …

The null splitting theorem (proved in math.DG/9909158) is discussed. As an application, a uniqueness theorem for Minkowski space and for de Sitter space associated with the occurrence of null lines (inextendible globally achronal null…

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…

The space ML(F) of measured geodesic laminations on a given closed hyperbolic surface F has a canonical linear structure arising in fact from different sources in 2-dimensional hyperbolic (earthquake theory) or complex projective (grafting)…

We consider Gowdy spacetimes under the assumption that the spatial hypersurfaces are diffeomorphic to the torus. The relevant equations are then wave map equations with the hyperbolic space as a target. In an article by Grubisic and…

We present a model of the gravitational field based on two symmetric tensors. Gravity is affected by the new field, but outside matter the predictions of the model coincide exactly with general relativity, so all classical tests are…

The geodesic properties of the extraordinary vacuum string solution in (4+1) dimensions are analyzed by using Hamilton-Jacobi method. The geodesic motions show distinct properties from those of the static one. Especially, any freely falling…

Consider the semialgebraic structure over the real field. More generally, let an ominimal structure be over a real closed field. We show that a definable metric space X with a definable metric d is embedded into a Euclidean space so that…

The large-scale geometry of hyperbolic metric spaces exhibits many distinctive features, such as the stability of quasi-geodesics (the Morse Lemma), the visibility property, and the homeomorphism between visual boundaries induced by a…

Global visibility of naked singularities is analyzed here for a class of spherically symmetric spacetimes, extending previous studies - limited to inhomogeneous dust cloud collapse - to more physical valid situations in which pressures are…

We generalize the action for point particle motion to a double field theory background. After deriving the general equations of motion for these particle geodesics, we specialize to the case of a cosmological background with vanishing…

We study the metric and topological properties of the space $\mathscr{D}(G)$ of left-invariant hyperbolic pseudometrics on the non-elementary hyperbolic group $G$ that are quasi-isometric to a word metric, up to rough similarity. This space…

We present a review of the two prominent singularity theorems due to Penrose and Hawking, as well as their physical interpretation. Their usage is discussed in detail for the Schwarzschild spacetime with positive and negative mass. First,…

We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the time- and…

In this paper we analyse Abelian diagonal orthogonally transitive spacetimes with spacelike orbits for which the matter content is a stiff perfect fluid. The Einstein equations are cast in a suitable form for determining their geodesic…

Since their introduction by Thurston, geodesic laminations on hyperbolic surfaces occur in many contexts. In this paper, we propose a generalization of geodesic laminations on locally CAT(0), complete, geodesic metric spaces, whose boundary…

In a closed fibered hyperbolic 3-manifold M, the inclusion of a fiber S, with S and M lifted to the universal covers gives an exponentially distorted embedding of the hyperbolic plane into hyperbolic 3-space. Nevertheless, Cannon and…

In this article we introduce a hyperbolic metric on the (normalized) space of stability conditions on projective K3 surfaces $X$ with Picard rank $\rho (X) =1$. And we show that all walls are geodesic in the normalized space with respect to…

We consider spherically symmetric spacetimes with matter whose timelike flow is assumed to be shear-free. A number of results on the formation and visibility of spacetime singularities is proven, with the main one being that shear-free…

This is just to point out that the Nariai metric is the first example of the singularity free expanding perfect fluid cosmological model satisfying the weak energy condition, $\rho>0, \rho+p=0$. It is a conformally non-flat Einstein space.

The existence of two metrics in massive gravity theories in principle allows solutions where there are singularities in new scalar invariants jointly constructed from them. These configurations occur when the two metrics differ…