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I Killing Vector Of Static Spacetime

  1. Apr 3, 2016 #1

    I am reading through some GR lecture notes and have come across the following:

    "A spacetime is static if there exists a coordinate chart where:

    0gμν = 0
    g0i = 0

    This spacetime admits a Timelike Killing vector X that satisfies:

    XβXγ] = 0 "

    How do I go about proving that this relation is true?


  2. jcsd
  3. Apr 3, 2016 #2


    Staff: Mentor

    Have you tried expanding out the relation that ##X## has to satisfy? Do any terms drop out or cancel because of the properties that the coordinate chart satisfies?
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