Is frame dragging a function of varying relationships to a mass field?

[Questioner]

Is frame dragging a function of varying relationships to a mass field?

Per a rotating mass:

A rotating body has more linear movement characteristics the further one is from its center.

So the/a passing 'with' rotation photon experiences a mass moving more in tandem/at-rest with it.
The 'against' rotation photon experiences a mass moving in opposition/relative to it.

I suppose the 'with' rotation photon is closer to experiencing the rotating mass at rest &
the 'against' photon experiences a moving & thereby greater relative mass body?

Does either photon gain or lose energy (mass? frequency?) from their trajectory relationship?

Does the rotating mass lose or gain angular momentum from either photon [or mass body]?