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Jun 10, 2017 at 17:08 comment added Cham The start premise is wrong, or just an over simplification, or an hypothsis at best if you prefer. So no wonders you arrive at the "no pressure" result since it's already implied from the start. The gas of particles with "internal" interactions don't have this free particles energy-momentum tensor. Think of a VanderWalls gas for example, which have short range interactions. Its energy-momentum tensor is certainly not like this simple form. So I think that the OP question is a sensible one, and it's still debated even today from a "gravity back reaction" view point.
Sep 27, 2014 at 14:34 vote accept John Eastmond
Sep 28, 2014 at 18:28
Sep 26, 2014 at 13:51 history answered John Rennie CC BY-SA 3.0