hi, i need to calculate the killing vector fields for axial symmetry for a project so i can study the galaxy rotation curves. i am assuming the galaxy to be a flat disk, in addition to being axially symmetric. so i figured that the killing vector fields with respect to which the metric manifold on the galaxy will be unchanged are: firstly, i'm using cylindrical coordinates: (t,r,z,phi) t=time (3+1) d(phi) (for axial symmetry) where phi is the angle and d(z) because the galaxy is a flat disk i don't know if there will be other killing vector fields. the problem is that i don't know of a systematic way to calculate them. thanks for the help!