  A four-index tensor is constructed with terms both quadratic in the Riemann
tensor and linear in its second derivatives, which has zero divergence for
space-times with vanishing scalar curvature. This tensor reduces in vacuum to
the Bel-Robinson tensor. Furthermore, the completely timelike component
referred to any observer is positive, and zero if and only if the space-time is
flat (excluding some unphysical space-times). We also show that this tensor is
the unique that can be constructed with these properties. Such a tensor does
not exist for general gravitational fields. Finally, we study this tensor in
several examples: the Friedmann-Lema\^{\i}tre-Robertson-Walker space-times
filled with radiation, the plane-fronted gravitational waves, and the Vaidya
radiating metric.
