Causal Structure - Introduction - Causal Relations

Causal Relations

There are two types of causal relations between points and in the manifold .

  • chronologically precedes (often denoted ) if there exists a future-directed chronological (timelike) curve from to .
  • causally precedes (often denoted or ) if there exists a future-directed causal (non-spacelike) curve from to or .
  • strictly causally precedes (often denoted ) if there exists a future-directed causal (non-spacelike) curve from to .
  • horismos (often denoted or ) if and .

These relations are transitive:

  • , implies
  • , implies

and satisfy

  • implies (this follows trivially from the definition)
  • , implies
  • , implies

Read more about this topic:  Causal Structure, Introduction

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