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Waves in GR

  1. Feb 9, 2008 #1

    Dale

    Staff: Mentor

    How do you get gravitational waves or gravitons out of the EFE? It certainly doesn't look like a wave equation. Are there some second derivatives hidden in the Einstein tensor?
     
  2. jcsd
  3. Feb 9, 2008 #2

    cristo

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, there are second derivatives hidden in the Einstein tensor. If you think of what it's made up of: Riemann tensor, which is made up of derivatives of the Christoffel symbols, which are made up of derivatives of the metric tensor.
     
  4. Feb 9, 2008 #3
    You don't get gravitons out of Einstein's field equations; those only show up when you attempt to generate an effective quantum field theory that includes gravity.
    For gravitational waves, the easiest method would be to use the weak-field equations in the transverse gauge, and set the energy-momentum tensor to zero (which corresponds to solutions of the equation infinitely far away from the originating source term). After a few lines of basic tensor analysis, you're left with the curved-spacetime version of the homogeneous wave equation, in terms of the d'Alembertian operator.
     
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