In the study of Lorentzian manifold spacetimes there exists a hierarchy of causality conditions which are important in proving mathematical theorems about the global structure of such manifolds. These conditions were collected during the late 1970s.
The weaker the causality condition on a spacetime, the more unphysical the spacetime is. Spacetimes with closed timelike curves, for example, present severe interpretational difficulties. See the grandfather paradox.
It is reasonable to believe that any physical spacetime will satisfy the strongest causality condition: global hyperbolicity. For such spacetimes the equations in general relativity can be posed as an initial value problem on a Cauchy surface.
Read more about Causality Conditions: The Hierarchy, Non-totally Vicious, Chronological, Causal, Strongly Causal, Stably Causal, Globally Hyperbolic
Famous quotes containing the words causality and/or conditions:
“Time, space, and causality are only metaphors of knowledge, with which we explain things to ourselves.”
—Friedrich Nietzsche (1844–1900)
“When and under what conditions is the black man to have a free ballot? When is he in fact to have those full civil rights which have so long been his in law?”
—Benjamin Harrison (1833–1901)