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Orbits of a Killing vector field

  1. Mar 12, 2012 #1
    I was wondering what the orbits of a Killing vector field are. Do you have any good sources or reading material for this?
  2. jcsd
  3. Mar 12, 2012 #2


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    http://www.lightandmatter.com/html_books/genrel/ch07/ch07.html#Section7.1 [Broken]
    Last edited by a moderator: May 5, 2017
  4. Mar 14, 2012 #3
    Given a (not necessarily Killing) vector field [itex]V^\mu(x)[/itex], its "orbits" are solutions [itex]Z^\mu(\lambda)[/itex] to the differential equation [itex]\dot{Z}^\mu(\lambda) = V^\mu(Z(\lambda))[/itex], where the dot is a [itex]\lambda[/itex] derivative. Intuitively, an orbit just "follows the little arrows of the vector field".

    That's all there is to it.
  5. Mar 14, 2012 #4

    Thanks Sam. I'll do some calculations with this definition and come back if I have further clarifications.
  6. Mar 14, 2012 #5
    Hall's book on symmetries in GR is my favorite, I'd go so far as to say, I love it.
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