Boj. Tupper, CONFORMAL-SYMMETRIES OF CONFORMAL-REDUCIBLE SPACETIMES WITH NONZERO WEYL TENSOR, Classical and quantum gravity, 13(6), 1996, pp. 1679-1687
By using the fact that 2 + 2 reducible spacetimes which are not confor
mally Bat can admit no proper conformal Killing vectors, it is shown h
ow all conformal symmetries of 2 + 2 conformal reducible spacetimes, i
ncluding spherically symmetric and plane symmetric spacetimes, with no
n-zero Weyl tensor may be found. The method applies to any spacetime w
hich is conformal to a 2 + 2 reducible spacetime with non-zero Weyl te
nsor.