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Kretschmann Scalar

  1. Jun 11, 2009 #1
    The Kretschmann scalar (the full contraction of the Reimann tensor K = R_abcd R^abcd) is often used to identify singularities - i.e. for a Schwarzschild black hole, K \propto 1/r^6, so we have a singularity at r=0, but not at the Schwarzschild horizon).

    Clearly, as r->\infinity, K->0. Is K=0 a measure of flat spacetime in general? Is there a reference that shows this?

    Cheers
     
  2. jcsd
  3. Jun 11, 2009 #2

    George Jones

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    The person best able to answer this has stopped posting, but, from previous posts of his, the answer is "No." There are pp-waves that have curvature singularities, and that have K = 0. I suspect that this somewhere in Exact Solutions of Einstein's Field Equations by Hans Stephani, Dietrich Kramer, Malcolm MacCallum, and Cornelius Hoenselaers.

    See 4. in
    https://www.physicsforums.com/showthread.php?p=1351759#post1351759

    1. in
    https://www.physicsforums.com/showthread.php?p=1124707#post1124707 [Broken]

    and the last paragraph of (the first post)
    https://www.physicsforums.com/showthread.php?p=1176876#post1176876
     
    Last edited by a moderator: May 4, 2017
  4. Jun 12, 2009 #3

    George Jones

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    According to Hawking and Ellis, page 260, it was pointed out by Penrose that curvature can be non-zero even when stuff like K is zero.
     
  5. Jun 12, 2009 #4
    Thanks George - will check it out.
     
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