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
Famous quotes containing the word hierarchy:
“In the world of the celebrity, the hierarchy of publicity has replaced the hierarchy of descent and even of great wealth.”
—C. Wright Mills (19161962)
“In a hierarchy every employee tends to rise to his level of incompetence.”
—Laurence J. Peter (19191990)