# Angular momentum in curved spacetime

• nickyrtr
In summary, the transformation of an object's angular momentum vector when moving in curved spacetime involves the curvature tensor and is parallel transported along the worldline of the gyroscope. This was demonstrated by Gravity Probe B in measuring the geodetic effect. The transformation is considered as a two-form, specifically the angular momentum two-form or bivector r^p, using the wedge product and including the radial vector and linear momentum, rather than the traditional 3-dimensional form of r x p with the cross product.
nickyrtr
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.

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.

## 1. What is angular momentum in curved spacetime?

Angular momentum in curved spacetime is a physical quantity that describes the rotational motion of an object in a curved space. It takes into account both the angular momentum of the object and the effects of the curvature of space on that motion.

## 2. How is angular momentum in curved spacetime different from angular momentum in flat spacetime?

In flat spacetime, angular momentum is conserved and does not depend on the position or orientation of the object. However, in curved spacetime, the curvature of space can affect the motion of the object and change its angular momentum.

## 3. What are some applications of studying angular momentum in curved spacetime?

Understanding angular momentum in curved spacetime is important in many areas of physics, including general relativity, quantum mechanics, and astrophysics. It is also used in the study of celestial bodies, such as planets, stars, and galaxies.

## 4. How is angular momentum conserved in curved spacetime?

Angular momentum is conserved in curved spacetime, just as it is in flat spacetime. However, the conservation law is modified to take into account the effects of the curvature of space on the motion of the object.

## 5. Can angular momentum in curved spacetime be measured?

Yes, angular momentum in curved spacetime can be measured using various techniques, such as measuring the rotation of celestial bodies or analyzing the behavior of particles in a curved space. However, due to the complex nature of curved spacetime, these measurements may be more challenging than in flat spacetime.

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