[saspinski (OP)]

I am trying to understand the so called “momentary commoving reference frame” (MCRF) used for the energy-moment tensor in GR.
Using the example of the suspension system of a car, each cubic element around a point of the spring has a stress tensor changing with time, as the car moves trough an off road way. The elements have different velocities because they vibrate due to the loads and elastic constant of the spring. Velocity * spring density = p (momentum per volume). p_x, σ_xx,σ_yx and σ_zx form one of the lines of the 4x4 energy-moment tensor.   
The importance of p and tensions in elasticity relates to the equation: F_x = ∂σ_xx/∂x + ∂σ_yx/∂y + ∂σ_zx/∂z, where Fx = ∂p_x/∂t.
Similar for the other axis.
It is not required that the elements are momentarily at rest to that analysis.
I assume that MCRF is necessary in relativity because different speeds would require Lorentz transformation between the elements, and it must be avoided.

[Bill S]

Not something I could help with, but in the seeming absence of informed replies, it's worth asking if you have been here.

https://physics.stackexchange.com/questions/93022/exact-definition-of-momentarily-comoving-reference-frame-mcrf