Domain of Dependence
- 1 February 1970
- journal article
- conference paper
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 11 (2) , 437-449
- https://doi.org/10.1063/1.1665157
Abstract
The various properties of the domain of dependence (Cauchy development) which have been found particularly useful in the study of gravitational fields are reviewed. The basic techniques for constructing proofs and counterexamples are described. A new tool—the past and future volume functions—for treating certain global properties of space-times is introduced. These functions are used to establish two new theorems: (1) a necessary and sufficient condition that a space-time have a Cauchy surface is that it be globally hyperbolic; and (2) the existence of a Cauchy surface is a stable property of space-times.Keywords
This publication has 13 references indexed in Scilit:
- The existence of cosmic time functionsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1969
- Spinor Structure of Space-Times in General Relativity. IJournal of Mathematical Physics, 1968
- The occurrence of singularities in cosmology. ɪɪɪ. Causality and singularitiesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1967
- On the structure of causal spacesMathematical Proceedings of the Cambridge Philosophical Society, 1967
- The occurrence of singularities in cosmology. IIProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1966
- The occurrence of singularities in cosmologyProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1966
- Gravitational Collapse and Space-Time SingularitiesPhysical Review Letters, 1965
- Essais de géométrie riemannienne hyperbolique globale. Applications à la relativité généraleAnnales de l'institut Fourier, 1963
- Line Element Fields and Lorentz Structures on Differentiable ManifoldsAnnals of Mathematics, 1955
- On C 1 -ComplexesAnnals of Mathematics, 1940