Frame Dragging Effect vs Spin Orbit Coupling in GR

[cosmik debris]

I believe that GR cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum. The exchange of orbital and intrinsic angular momentum requires that the momentum tensor be non-symmetric during the exchange. GR cannot accommodate a non-symmetric momentum tensor because the Ricci tensor is symmetric in Riemannian geometry.

My question, assuming what I said above is true, is the frame-dragging effect verified by Gravity Probe B a result of something other than spin-orbit coupling, because on the surface it looks similar.

Thanks.

 

[PeterDonis]

I believe that GR cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum.

What do you mean by "classical intrinsic angular momentum"?

The exchange of orbital and intrinsic angular momentum requires that the momentum tensor be non-symmetric during the exchange.

What "momentum tensor" are you talking about?

 

[Dale]

GR cannot accommodate a non-symmetric momentum tensor because the Ricci tensor is symmetric in Riemannian geometry.

That is not at all what this implies. This means that the theory does not introduce any asymmetry. It is perfectly feasible for the source to introduce asymmetry.

 

[stevendaryl]

What "momentum tensor" are you talking about?

I think he's talking about the stress-energy tensor. There is a line in Wikipedia saying this:

"In some alternative theories like Einstein–Cartan theory, the stress–energy tensor may not be perfectly symmetric because of a nonzero spin tensor, which geometrically corresponds to a nonzero torsion tensor."

https://en.wikipedia.org/wiki/Stress–energy_tensor

I never understood the details, either why spin can make the stress-energy tensor asymmetric, or why regular GR would have to be modified to account for it.

 

[stevendaryl]

I see that this has been discussed previously (I was the one who started the thread) without coming to a clear conclusion:

https://www.physicsforums.com/threads/spin-density-and-non-symmetric-stress-energy-tensor.615574/

 

[PeterDonis]

I see that this has been discussed previously

Post #5 in that thread confirms what I thought, that there is no "gravitational spin-orbit coupling" in GR.

is the frame-dragging effect verified by Gravity Probe B a result of something other than spin-orbit coupling

Yes, since, as above, there is no spin-orbit coupling in GR.

 

[PeterDonis]

I believe that GR cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum.

If "classical intrinsic angular momentum" just means the spin of some body like the Earth whose internal structure we are not modeling, then this statement would be very surprising, since Newtonian gravity, which is a valid approximation to GR under appropriate conditions, can describe this just fine (for example, the slowing down of the Earth's rotation and the increase in the Moon's orbital radius due to tidal interactions).

 

[cosmik debris]

I think he's talking about the stress-energy tensor. There is a line in Wikipedia saying this:

"In some alternative theories like Einstein–Cartan theory, the stress–energy tensor may not be perfectly symmetric because of a nonzero spin tensor, which geometrically corresponds to a nonzero torsion tensor."

https://en.wikipedia.org/wiki/Stress–energy_tensor

I never understood the details, either why spin can make the stress-energy tensor asymmetric, or why regular GR would have to be modified to account for it.

Yes, I was thinking about this in relation to Einstein-Cartan theory. I see I will have to do a lot more reading but thanks for all the replies anyway.

Cheers

 

[cosmik debris]

If "classical intrinsic angular momentum" just means the spin of some body like the Earth whose internal structure we are not modeling, then this statement would be very surprising, since Newtonian gravity, which is a valid approximation to GR under appropriate conditions, can describe this just fine (for example, the slowing down of the Earth's rotation and the increase in the Moon's orbital radius due to tidal interactions).

Yes, that was my confusion, I see that the Earth-Moon system behaves in he way you have described and was trying to understand what this had to do with the non spin-orbit coupling in GR. I see that I was totally off track and need to do a lot more reading. Thanks for your input anyway.

Cheers