Invariants of the Riemann tensor for class B warped product space-times

We use the computer algebra system GRTensorII to examine invariants polynom ial in the Riemann tensor for class B warped product space-times - those wh ich can be decomposed into the coupled product of two 2-dimensional spaces, one Lorentzian and one Riemannian, subject to the separability of the coup ling ds(2) = ds(Sigma 1)(2) (u, upsilon) + C (x(gamma))(2) ds(Sigma 2)(2) ( theta, phi), with C (x(gamma))(2) = r(u, upsilon)(2)w(theta, phi)(2) and si g(Sigma(1)) = 0, sig(Sigma(2)) = 2 epsilon (epsilon = +/-1) for class B-1 s pace-times and sig(Sigma(1)) = 2 epsilon, sig(Sigma(2)) = 0 for class B-2. Although very special, these spaces include many of interest, for example, all spherical, plane, and hyperbolic space-times. The first two Ricci invar iants along with the Ricci scalar and the real component of the second Weyl invariant J alone are shown to constitute the largest independent set of i nvariants to degree five for this class, Explicit syzygies are given for ot her invariants up to this degree. It is argued that this set constitutes th e largest functionally independent set to any degree for this class, and so me physical consequences of the syzygies are explored. (C) 1998 Elsevier Sc ience B.V.