If I compress an elastic solid I will strain the material in the direction of the force and therefore do work that is stored as potential energy in the material. The resulting material will have no velocity, but its rest mass will increase, presumably causing increased gravitational bending of spacetime.
Assume I have a cube of an elastic material aligned with some Cartesian coordinates in a natural way. If I compress it along the x direction, placing it under mechanical compression, will the stress mass energy tensor increase its 0,0 component or its 1,1 component?
Now, if the answer is the 0,0 component, and if I then look at the same situation from a coordinate system rotated 45 deg from the original system about an axis perpendicular to the compression force - say about z, then the resulting system will have sheer stress on faces defined by constant x and y values in the new system, at least the force will no longer be normal to them. Are these stresses accounted for in the 0,0 component of the stress mass energy tensor or in the (1,2), (2,1) components.
If in the 0,0 component why is the 1,2 component labeled as sheer stress. In other words, when a sheer stress or any other stress is applied, the velocity of the material remains zero once the stress is established. So how can a sheer stress also be a momentum flux?
Questions are not rhetorical. Terribly confused. Thanks.