# Ricci Equal to {}

1. Jul 28, 2013

### Philosophaie

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. Jul 28, 2013

### WannabeNewton

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?

3. Jul 28, 2013

### Philosophaie

Looking for a real world metric that will produce a non-zero Ricci, Ricci Scalar and therefore a Energy-Momentum Tensor.

4. Jul 28, 2013

### WannabeNewton

5. Jul 28, 2013

### Philosophaie

Thanx

6. Jul 28, 2013

### Staff: Mentor

FLRW as WannabeNewton mentioned. Also, any interior Schwarzschild solution.

7. Jul 29, 2013

### andrien

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.