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Ricci Equal to {}

  1. Jul 28, 2013 #1
    The Schwarzenchild and the Kerr Metrics for Black Holes give a Ricci = {}.

    What does a Ricci Flat mean?

    It obliviously has no momentum density or flow because the Stress-Momentum Tensor is also = {}.

    It could mean freefall geodesic into a Black Hole?

    or it also could be in some sort of stable orbit: circular, ellipse or hyperbolic.

    Any suggestions?
     
  2. jcsd
  3. Jul 28, 2013 #2

    WannabeNewton

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    Ricci flat just means ##R_{ab} = 0## identically. In the context of GR it represents vacuum solutions to the field equations. Are you looking for something specific?
     
  4. Jul 28, 2013 #3
    Looking for a real world metric that will produce a non-zero Ricci, Ricci Scalar and therefore a Energy-Momentum Tensor.
     
  5. Jul 28, 2013 #4

    WannabeNewton

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  6. Jul 28, 2013 #5
    Thanx
     
  7. Jul 28, 2013 #6

    Dale

    Staff: Mentor

    FLRW as WannabeNewton mentioned. Also, any interior Schwarzschild solution.
     
  8. Jul 29, 2013 #7
    Just as a side note,in 4-D vanishing of Ricci curvature tensor does not imply flat spacetime.It is the Riemann tensor which describes it.However in 3-D,if ricci is zero then riemann curvature also vanishes and so in 2-D vanishing of scalar curvature implies flatness.No further need of ricci or riemann curvature tensor.
     
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