I've been studying Misner, Thorne, and Wheeler's Gravitation and a thought had occurred to me: if black holes had angular momentum, why wouldn't this cause torsion in spacetime? If this is true, wouldn't we need to reject Einstein's field equation and "get" a "new one"?

 

Maybe I jumped to the conclusion too soon thinking "Aha, angular momentum of a black hole affects spacetime, thus spacetime would be 'twisted' or at least victim of some sort of torsion." I was also considering this in terms of quantized spacetime, which may have caused the problem(!).

isn't a twisted spacetime around spinning objects PREDICTED by GR? i thought that was what gravity probe b was trying to test.

From my understanding, grav probe b was trying to prove the equivalence principle by use of gyros.

 

But doesn't the Ricci tensor "forbid" the torsion of the manifold (spacetime)? That was my impression.

i also thought GR predicted a twist and space time and that gravity probe b was trying to detect it.

 

Yup here we go. http://en.wikipedia.org/wiki/Gravity_Probe_B

But doesn't the Ricci tensor "forbid" the torsion of the manifold (spacetime)? That was my impression.

 

Yes, a Ricci tensor is symmetric [imath]R_{\alpha\beta} = R_{\beta\alpha}[/imath], and therefore torsionless.