Stably Causal
A manifold satisfying any of the weaker causality conditions defined above may fail to do so if the metric is given a small perturbation. A spacetime is stably causal if it cannot be made to contain closed causal curves by arbitrarily small perturbations of the metric. Stephen Hawking showed that this is equivalent to:
- There exists a global time function on . This is a scalar field on whose gradient is everywhere timelike and future-directed. This global time function gives us a stable way to distinguish between future and past for each point of the spacetime (and so we have no causal violations).
Read more about this topic: Causality Conditions
Famous quotes containing the word causal:
“There is the illusion of time, which is very deep; who has disposed of it? Mor come to the conviction that what seems the succession of thought is only the distribution of wholes into causal series.”
—Ralph Waldo Emerson (1803–1882)