Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor

    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


    User Avatar
    Science Advisor

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


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook