Terrific paper by @johncarlosbaez and Ted Emory, explaining the meaning of the Einstein field equations for general relativity: http://math.ucr.edu/home/baez/einstein/einstein.pdf …pic.twitter.com/65fMVQR2tH
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Mathematical physicist and mentor to mathematically talented youth. Talent is that which bridges the gap between what can be taught and what must be learned.
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Terrific paper by @johncarlosbaez and Ted Emory, explaining the meaning of the Einstein field equations for general relativity: http://math.ucr.edu/home/baez/einstein/einstein.pdf …pic.twitter.com/65fMVQR2tH
The Cartanian formulation of Newtonian gravity shows that the local form of the classical inverse square law (i.e., the Poisson equation on the Newtonian gravitational potential) has precisely the same interpretation. The only difference is that the pressures don't contribute.
Nice! I never got that far with the Cartan formulation of Newtonian gravity. But since pressure's contribution is suppressed by a factor of c squared, it must go away in the Newtonian limit.
Yes, exactly. In fact, if you write the Einstein equation as "Ricci curvature = 8*pi*G*(trace-reversed stress-energy)," then both sides have a smooth Newtonian limit, which is the Poisson equation. (Pressures don't matter, because the metric degenerates in the Newtonian limit.)
Do you have a favorite exposition of the Cartanian formulation of Newtonian gravity? This paper has lots of references, but I don't know what I'd like: https://arxiv.org/abs/1811.03446 The paper itself is too full of indices, too short of words for me.
The Wikipedia article http://bit.ly/2J5StwZ is a good intro, and the best of the references it includes is the one to Trautman -- first rate. (If you read German comfortably, though, then there's a paper of Ehlers that I'd recommend above all others. That guy was great.)
I'm a big fan of Trautman... and I had the luck to have a conversation with him. So that sounds good. (I hadn't known Ehlers died! I've been out of the quantum gravity / GR scene for too long.)
Ehlers' death was a great loss. He was one of the very finest relativity theorists of the latter half of the 20th century. And his exposition of that theory, referred to in that Wikipedia article on the Newton-Cartan formulation, is a masterpiece. Simply not to be missed.
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