Collineations of Ricci tensor for cylindrical spacetimes

A complete classification of cylindrically symmetric static Lorentzian manifolds according to their Ricci collineations (RCs) is provided. It is found that the Lie algebras of the RCs of these manifolds (for non-degenerate Ricci tensor) has dimension ranging from 3 to 10 excluding 8 and 9. The comparison of the RCs with the Killing vectors (KVs) and homothetic motions (HMs) is made. Corresponding to each Lie algebra there arise highly non-linear differential constraints on the metric coefficients. These constraints are solved to construct examples which include some exact solutions admitting proper RCs. Their physical interpretation is given. The classification of plane symmetric static spacetimes (Farid et al., J. Math. Phys., 36 (1995) 5812) emerges as a special case of this classification when the cylinder is unfolded.