In Einstein's field equations, the pressure terms on the diagonal of the stress-energy tensor contribute like energy density to the "Komar mass", and help determine the curvature and hence the gravitational effect. I believe that these terms represent "rate of exchange of x-component of momentum in the x-direction per unit area" and so on for y and z as well. As far as I can see these terms do not appear to be the density of a conserved quantity. For example, one could have two masses held apart by a nearly massless rigid rod, then move the rod aside, and the pressure in the rod would just drop to zero, without "going anywhere". Is this correct or have I missed something? (With a more realistic description of the removal process, I suspect that for a real not quite rigid material there would be a small amount of ordinary energy which would turn into kinetic energy of flexing, oscillation or heat within the removed rod, but as far as I can see this energy could be negligible compared with the pressure times the volume). If that is correct, I find it hard to understand how this term could really contribute either to the gravitational effect of the system or to the effective total energy.