Journal ArticleDOI
The geometry of the space of null geodesics
TLDR
In this paper, the topology and geometry of the space of null geodesics N of a space-time M are used to study the causal structure of the time itself.Abstract:
The topology and geometry of the space of null geodesics N of a space‐time M are used to study the causal structure of the space‐time itself. In particular, the question of whether the topology of N is Hausdorff or admits a compatible manifold structure carries information on the global structure of M, and the transversality properties of the intersections of skies of points tell whether the points are conjugate points on a null geodesic.read more
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Gravitational Lensing from a Spacetime Perspective
TL;DR: In this paper, the theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations, where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature, and the basic equations and relevant techniques for calculating the position, shape, and brightness of images in an arbitrary general-relativistic spacetime.
Posted Content
Gravitational Lensing from a Spacetime Perspective
TL;DR: The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations, and includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images.
Journal ArticleDOI
Geodesic connectedness of semi-Riemannian manifolds
TL;DR: The question whether a Riemannian manifold is geodesically connected can be studied from geometrical as well as variational methods, and accurate results can be obtained by using the associated distance and related properties of the positive-definiteness.
Journal ArticleDOI
Linking, Legendrian Linking and Causality
José Natário,Paul Tod +1 more
TL;DR: In this article, it was conjectured by Low that for d = 2$ two events x and y are causally related if and only if X and Y are linked (in an appropriate sense), and they used the contact structure and knot polynomial calculations to prove this conjecture in certain particular cases.
Journal ArticleDOI
Stable singularities of wave-fronts in general relativity
TL;DR: In this article, it was shown that the space of null geodesics N of a space-time M, considered as a contact manifold, provides a natural setting for an efficient study of the stable singularities arising in the time evolution of wavefronts.
References
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Book
The Large Scale Structure of Space-Time
TL;DR: In this paper, the authors discuss the General Theory of Relativity in the large and discuss the significance of space-time curvature and the global properties of a number of exact solutions of Einstein's field equations.
Book
Techniques of Differential Topology in Relativity
TL;DR: In this article, the specialist in relativity theory with some global techniques for the treatment of space-times and will provide the pure mathematician with a way into the subject of general relativity.
Journal ArticleDOI
A Remarkable Property of Plane Waves in General Relativity
TL;DR: In this article, the complete general-relativistic plane-wave space-times (gravitational, electromagnetic, or both) are examined in relation to the focusing effect they exert on null cones.
Journal ArticleDOI
Ideal points in space-time
TL;DR: In this article, it is shown that domains of dependence can be characterized in terms of ideal points, and this makes possible an extension of the domain-of-dependence concept to causal spaces.