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Introduction to the mathematics of general relativity
About: Introduction to the mathematics of general relativity is a research topic. Over the lifetime, 2583 publications have been published within this topic receiving 73295 citations.
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TL;DR: In this article, the concept of ''future timelike infinity'' for certain space-times is defined and applied to many exact and approximate solutions of the Einstein equations. But some physical restrictions are necessary.
Abstract: We use a projective structure to make precise the concept of ``future timelike infinity'' for certain space‐times. We apply our definitions to many exact and approximate solutions of the Einstein equations. Some physical restrictions are necessary.
15 citations
01 Jun 2000
TL;DR: In this paper, the singular hyperbolic equations of the Einstein equations are used to construct large families of solutions of the general relativity equations with singularities of a simple type by solving singular hyper-bolic systems.
Abstract: An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime singularities is naturally related to blow-up phenomena for nonlinear hyperbolic systems. These connections are explained and recent progress in applying the theory of hyperbolic equations in this field is presented. A direction which has turned out to be fruitful is that of constructing large families of solutions of the Einstein equations with singularities of a simple type by solving singular hyperbolic systems. Heuristic considerations indicate, however, that the generic case will be much more complicated and require different techniques.
15 citations
TL;DR: In this article, it was shown that the theorem of Duff on the existence and uniqueness of solutions to linear characteristic initial value problems holds in the case of linearized characteristic evolution in Bondi-Sachs coordinates in general relativity.
Abstract: We show that the theorem of Duff on the existence and uniqueness of solutions to linear characteristic initial-value problems holds in the case of linearized characteristic evolution in Bondi-Sachs coordinates in general relativity. This represents the characteristic equivalent to the manifest existence and uniqueness of the case of standard Cauchy problems. This extends Sachs' original work on the characteristic approach to the Einstein equations, by considering a null-timelike approach rather than a null-asymptotic one.
15 citations
TL;DR: In this article, it is suggested how Bernhard Riemann might have discovered General Relativity soon after 1854 and how today's undergraduate students can be given a glimpse of this before, or independently of, their study of Special Relativity.
Abstract: It is suggested how Bernhard Riemann might have discovered General Relativity soon after 1854 and how today’s undergraduate students can be given a glimpse of this before, or independently of, their study of Special Relativity At the same time, the whole field of relativity theory is briefly surveyed from the space–time point of view
15 citations
Journal Article•
TL;DR: Gauthier-Villars as mentioned in this paper implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/conditions).
Abstract: © Gauthier-Villars, 1965, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section A » implique l’accord avec les conditions générales d’utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
15 citations