GR & Coriolis Forces: Inertial Trajectories & Resources

[dand5]

How does GR account for coriolis forces on a solid spherically symmetric body in a frame of reference where the solidy body rotation has been eliminated?
Are these trajectories inertial, as in if a free falling object has an initial velocity along the angle between the plane of rotation and the axis of rotation, are the coriolis trajectories geodesic paths?
Also please let me know of any good references that might help me
understand this.
Thanks in advance for any replies.

 

[my_wan]

How does GR account for coriolis forces on a solid spherically symmetric body in a frame of reference where the solidy body rotation has been eliminated?

It appears that you meant that solid body is in fact rotating then you attempt to define a frame of reference for which it is not rotating. First of all it is not possible to define such a frame of reference when each point in the body not only has a different frame of reference but the frame of reference for each point is constantly changing. By constantly changing frames of reference means that it is accelerating, i.e. constantly changing either direction or magnitude of motion. Note that acceleration is not relative. All observers regardless of the frame of reference agree on what is and isn't accelerating. Observers can only disagree on how much acceleration. The only frame of reference in which the body is not rotating is when the body is not rotating in any frame of reference meaning no coriolis forces.

 

[Jimmy Snyder]

Note that acceleration is not relative. All observers regardless of the frame of reference agree on what is and isn't accelerating.

This seems to fly in the face of the equivalence principle.

Observers can only disagree on how much acceleration.

This is better. There is a frame in which an observer would say that zero is how much. The observer attributes observations to the fact that there is a gravitational field.

There is a frame in which the rotation of the body is eliminated, but it is not an inertial frame.

 

[pervect]

My $.02

Relativity explains rotating frames with Christoffel symbols, but I don't really think that's the type of explanation that's being asked for here.

So let's go with the Newtonian explanation.

If you are on a rotating body, you experience a Coriolis pseudo-force if you adopt a rotating coordinate system.

If you are on a rotating body and you use a non-rotating coordinate system, there are no pseudo-forces, and the body that was experienceing the coriolis psuedo-force in the rotating coordinate system is seen to be moving in a straight line in the non-rotating coordiante system.

 

[my_wan]

Note that acceleration is not relative. All observers regardless of the frame of reference agree on what is and isn't accelerating.

This seems to fly in the face of the equivalence principle.

Why? I do not see how my statement implies that gravitational and inertial mass are not equivalent.

Observers can only disagree on how much acceleration.

There is a frame in which an observer would say that zero is how much. The observer attributes observations to the fact that there is a gravitational field.

Zero how? No wait, first you defined a frame with zero acceleration. Then you say the observer attributes the observations (observations presumably meaning g forces) to a gravitational field. So you have g forces with zero acceleration? If that's not a violation of the Principle of Equivalence I don't know what is. The only frame for which you could say acceleration is zero is one moving -at- the speed of light relative to the sphere. Even that is debatable.

There is a frame in which the rotation of the body is eliminated, but it is not an inertial frame.

Here you have conceded that the frame is not an inertial frame, which -means- it is accelerating.

To be fair it is possible to define a frame for which locally (meaning for a given infinitesimal point within the sphere) there is no rotation, only acceleration. This is what is meant when it's said that the Principle of Equivalence only applies locally. Globally it is always possible to to prove a spin even without referring to an outside frame of reference. Just try to operate a gyroscope inside such a spinning sphere.