Exact solutions for space-times admitting non-null special conformal Killing vectors (Q749878)

A special conformal Killing vector field (SCKV) \(\xi\) on a space-time (M,g) is defined by the condition \(L_{\xi}g=2\phi g\), grad \(\phi\) \(=0\), where \(\phi\) is a function on M. For space-times admitting SCKV with non- null gradient, a classification method is provided in terms of their isometry group.