The Hierarchy
There is a hierarchy of causality conditions, each one of which is strictly stronger than the previous. This is sometimes called the causal ladder. The conditions, from weakest to strongest, are:
- Non-totally vicious
- Chronological
- Causal
- Distinguishing
- Strongly causal
- Stably causal
- Causally continuous
- Causally simple
- Globally hyperbolic
We now give definitions of these causality conditions for a Lorentzian manifold . Where two or more are given they are equivalent.
Notation:
- denotes the chronological relation.
- denotes the causal relation.
(See causal structure for definitions.)
Read more about this topic: Causality Conditions
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