What is the Concept of Velocity and Acceleration in General Relativity?

[AngPhysics]

I am hoping someone can clarify some confusion I have. It is my understanding that there is no such thing as absolute velocity or acceleration in GR. If one observer is moving near the speed of light and the other is stationary each observer will see the other as in motion. But if they each throw a ball away from themselves the observer in motion, from my understanding, has a much larger gravitational potential than the observer at rest so their would be a feature that distinguishes between their "velocities".

 

[Orodruin]

It is my understanding that there is no such thing as absolute velocity or acceleration in GR.

While there is no absolute velocity, there is the concept of proper acceleration. This is the acceleration experienced by an observer following a particular world line and is invariant.

The same is true in SR.

from my understanding, has a much larger gravitational potential

Your understanding is wrong. The concept of relativistic mass does not apply to gravitation and how GR couples the metric to matter content. The correct statement is significantly more complicated. I suggest reading my insight article on relativistic mass, which is an obsolete concept not used by most physicists today.

 

[AngPhysics]

Thank you for the direction!