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Suppose one has a box moving through flat space-time with a stress energy tensor ##T^{ab}## that's non-zero inside the box and zero outside the box. How does one compute the normal forces on the faces of the box associated with it's motion? I am assuming that the normal forces are measured via a spring scale attached to the appropriate box face. I'm also interested in what other boundary conditions the stress-energy tensor must satisfy (if there are any).
If the metric at a box face is diag (-1,1,1,1) I'm pretty sure the answer is that the area of the box face multiplied by the pressure term ##T^{ii}## gives the normal force on the box wall. But this doesn't seem to be true in general.
If the metric at a box face is diag (-1,1,1,1) I'm pretty sure the answer is that the area of the box face multiplied by the pressure term ##T^{ii}## gives the normal force on the box wall. But this doesn't seem to be true in general.