Positivity properties of the Bel-Robinson tensor

The Bel-Robinson tensor is a rank 4 tensor constructed from the Weyl curvature tenser. It is well known that when it is contracted with four future-pointing vectors a non-negative value is always obtained. In this paper we investigate various cases in which the value zero is attained and show that it occurs in some situations where space-time is of an algebraically special type. This is of importance for expressions of gravitational energy related to the Bel-Robinson tenser. Some new invariant ways of classifying the Petrov type of space-times using the Bel-Robinson tenser are also presented. (C) 1998 American Institute of Physics. [S0022-2488(98)01204-3].