- #1
Phrak
- 4,267
- 6
The metric tensor is expressed in 10 independent elements. From this is obtained the Einstein equation once given 7 to 9 or so requirements imposed on the the connection and covariant derivative.
In my mind the Christoffel based covariant derivative is an ugly thing, good for a first attempt at understanding the connection between mass and gravity, but not the last word.
Instead: Can the relationship between curvature and stress-energy (The Einstein equuation,or something like it) be expressed in terms of oriented tensor densities with lower indices sans the goofey connections?
In my mind the Christoffel based covariant derivative is an ugly thing, good for a first attempt at understanding the connection between mass and gravity, but not the last word.
Instead: Can the relationship between curvature and stress-energy (The Einstein equuation,or something like it) be expressed in terms of oriented tensor densities with lower indices sans the goofey connections?
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