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Can you actually credibly find NS or even Euler’s equations as an effective theory from GR? Euler’s equations and NS have this pesky velocity field, which requ
by amluto 11d ago
Can you actually credibly find NS or even Euler’s equations as an effective theory from GR?
Euler’s equations and NS have this pesky velocity field, which requires the fluid’s state to be well described by a velocity at each point in space (and a density and a pressure, but I think GR has no problem with those). This means that you need some kind of interaction between particles to get them to exchange energy so that they thermalize instead of staying in the collisionless regime. (In other words, if you have two blobs of fluid collide, you need them to not go right through each other.) And I don’t think that GR is dissipating on the relevant scales.
As a real-world example, the universe contains neat structures (the horsehead nebula is a somewhat famous example) that are consistent with dark matter distributions that don’t really resemble fluids.
- immmmmm 9d agosorry for the late answer.. yes you can : https://arxiv.org/abs/1211.1983 https://arxiv.org/abs/1211.1983 but you might need to understand it in the context of holography in some frame you can recover non-relativistic symmetries, we got a paper on this back then, but so hardcore i only understand parts of it https://arxiv.org/abs/1205.5777 https://arxiv.org/abs/1205.5777
- immmmmm 9d agoPs: your comment on dissipation is good. But in certain frames GR can reproduce that. I’m far from an expert, but definition of energy is rly hard in GR (need both Noether thms). Research on the topic seems to have stalled a decade ago. Probably for a good reason.
- immmmmm 9d agoPS2: AdS/CFT (and we have at least one good candidate since Maldacena in string theory) correspondence shows that strongly coupled quantum systems in d dimensions are dual to *classical* gr systems in d+1 dimensions. Somewhere somehow dualities seems to relate completely different systems, that non relativistic dissipative systems happen in all generality somewhere in that mess is barely a surprise. I mean, if one believes ER=EPR GR and quantum mechanics are just the same thing.