Angular momentum in curved spacetime

Click For Summary
SUMMARY

The transformation of angular momentum in curved spacetime is fundamentally linked to the curvature tensor and the concept of parallel transport along a worldline. In the context of General Relativity (GR), the angular momentum is represented as a two-form, specifically a bivector denoted as r^p, where r is the radial vector and p is the linear momentum. This approach differs from the traditional 3-dimensional representation using the cross product. The principles discussed are exemplified by the Gravity Probe B experiment, which measured the geodetic effect through these transformations.

PREREQUISITES
  • Understanding of General Relativity (GR)
  • Familiarity with curvature tensors
  • Knowledge of angular momentum representations in physics
  • Basic concepts of parallel transport in differential geometry
NEXT STEPS
  • Study the role of curvature tensors in General Relativity
  • Explore the mathematical formulation of angular momentum as a two-form
  • Investigate the principles of parallel transport in curved spacetime
  • Review the findings of the Gravity Probe B experiment and its implications
USEFUL FOR

Physicists, students of General Relativity, and researchers interested in the dynamics of angular momentum in curved spacetime.

nickyrtr
Messages
93
Reaction score
1
When an object moves in curved spacetime, how does its angular momentum vector transform? My hunch is that the curvature tensor is involved somehow, but can't figure out an obvious equation for dLa/dxb. Probably I even wrote that derivative wrong .. sorry I'm a newbie at GR.
 
Physics news on Phys.org
The angular momentum is parallel transported along the worldline of the gyroscope. This is how Gravity Probe B measured the geodetic effect.
 
I believe it transforms as a two-form, i.e. one considers the angular momentum two-form or bivector r^p , where ^ is the wedge product, r is the radial vector, and p is the linear momentum, rather than the 3-d form r x p, where x is the cross prolduct.
 

Similar threads

  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 0 ·
Replies
0
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 19 ·
Replies
19
Views
3K
Replies
1
Views
2K
  • · Replies 38 ·
2
Replies
38
Views
4K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K