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]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Equations of Motion

**Physics Forums | Science Articles, Homework Help, Discussion**