If for the "geodesic" equation of motion we have the compact form:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \nabla _ u u =0 [/tex] usign the "Covariant derivative"... as a generalization of Newton equation with F=0 (no force or potential) [tex] \frac{du}{ds}=0 [/tex] where "u" is the 4-dimensional momentum...

My question is if we can put the Equation of motion [tex] \R _\mu \nu =0 [/tex] as the "LIe derivative" or " Covariant derivative" or another Tensor, vector or similar involving the "momentum density" [tex] \pi _a b [/tex] and the metric elements [tex] g_ ab [/tex]

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# Equations of Motion

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