Globally hyperbolic
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Globally hyperbolic (also global hyperbolicity) is a term describing the "causal structure" of a spacetime manifold in Einstein's theory of general relativity, or potentially in other metric gravitational theories.
Open sets are used in discussing the global hyperbolicity of spacetimes. An open set U is said to be globally hyperbolic if the following two conditions hold[1]
- For every pair of points
, 
is compact. Here 
is the future (past) of a set S in spacetime. - Strong causality holds on U. (No closed timelike curves).
Global hyperbolicity implies that there is a family of Cauchy surfaces for U. Essentially, it means that everything that happens on U is determined by the equations of motion, together with initial data specified on a surface.
[edit] See also
[edit] References
- ^ Stephen Hawking and Roger Penrose, The Nature of Space and Time, Princeton University Press, 1996.
- Hawking, Stephen; and Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time. Cambridge: Cambridge University Press. ISBN 0-521-09906-4.
