The standard form of the field equations is G = 8 pi T, where G is the Einstein tensor (roughly, the curvature of spacetime), and T is the stress-energy tensor (roughly, expressing mass and energy).
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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
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John Wheeler expressed the meaning of these equations beautifully: "Spacetime tells matter how to move; matter tells spacetime how to curve"
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But while that expression is beautiful, it's also rather imprecise. What I like about the Baez-Emory formulation is that it's also very simple, but is mathematically precise!
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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.
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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.
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Jinx
I just printed this 2006 paper yesterday while trying to understand implications of Sabine H’s recent post.pic.twitter.com/y8uTB5QESf
Thanks. Twitter will use this to make your timeline better. UndoUndo
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