A third-order curvature invariant in static spacetimes

We consider here the third-order curvature invariant I = R-mu nu p sigma;delta R-mu nu p sigma;delta in static spacetimes M = R x Sigma for which Sigma is conformally flat. We evaluate explicitly the invariant for the N-dimensional Majumdar-Papapetrou multi black-hole solution, confirming that I does indeed vanish on the event horizons of such black holes. Our calculations show, however, that alone the vanishing of I is not sufficient to locate an event horizon in non-spherically symmetric spacetimes. We also discuss some tidal effects associated with the invariant I.