It is reasonable to believe that any physical spacetime will satisfy the strongest causality condition : global hyperbolicity.
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There is a hierarchy of causality conditions, each one of which is strictly stronger than the previous.
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The weaker the causality condition on a spacetime, the more " unphysical " the spacetime is.
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Since the system cannot respond before the input is applied the following "'causality condition "'must be satisfied:
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A manifold satisfying any of the weaker causality conditions defined above may fail to do so if the metric is given a small perturbation.
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In the spirit of causal structure, Causality conditions has been recently created . contribs ) 21 : 41, 29 November 2007 ( UTC)
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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.
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However, one attempts to derive a world topology directly from a space-time structure ( a strong causality condition, such topologies coincide with a familiar manifold topology of a world manifold.
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