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How to check if Schwarschild space-time is locally minkowskian

  1. Jul 14, 2013 #1

    I would like to check that, ie if the tangent spacetime of schwarzschild can be linked to minkowski spacetime via a lorentz transformation.

    But i have a problem from the onset since the tangent space seems to me to exist only in exterior geometry. For example the tangent plane to a surface lies in embedding 3d space.

    Else how to find the tangent space given only interior coordinates and metric ?

  2. jcsd
  3. Jul 14, 2013 #2


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    All space-times are locally Minkowskian; just setup Riemann normal coordinates in an appropriate neighborhood of an event. This can be done generally for any space-time, not just Schwarzschild. You can't link the tangent space to space-time at an event to Minkowski space-time via a Lorentz transformation; I'm not sure where you even got that idea. The isomorphism between the tangent space at any event and Minkowski space-time can be obtained explicitly using basic linear algebra but it has nothing to do with Lorentz transformations.
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