- 3,507

- 26

I read in wikipedia that a manifold with more than three dimensions, like spacetime, is conformally flat if its Weyl tensor vanishes. I think all FRW metrics are conformally flat, so I guess our universe is conformally flat and that means a Weyl curvature=0 in our spacetime manifold, doesn't it?

But this seems at odds with the wikipedia definition of the Weyl tensor that says it expresses the tidal force a body feels in a geodesic, specifically the part about how the shape of the body distorts, i.e., the classic example of the sphere of balls initially at rest that changes its shape to an elipsoid in the presence of gravity. So there seems to be a Weyl curvature there different from 0.

Also in Penrose's Road to reality book, he explains that the outward deflection of light rays outside the sun's rim is an example of the Weyl curvature.

What am I not getting right here?