Suppose that ξ is a Killing vector, so that it satisfies the equation:
ξa||b + ξb||a = 0.
You have previously shown that ξ satisfies the equation:
ξa b c = Rd ξd .
Derive the maximum number of independent Killing vector fields that can exist in a spacetime of dimension N . Compare the number of Killing vectors that exist in some of the metrics we have considered to the maximum and try to break the isometry group into smaller parts for these spacetimes. Also, for each spacetime you consider, analyze the isometry group for significant subspaces, and comment briefly on how these might have helped in arriving at the particular spacetime.