  We derive a general integral formula on an embedded hypersurface for general
relativistic space-times. Suppose the hypersurface is foliated by
two-dimensional compact ``sections'' $S_s$. Then the formula relates the rate
of change of the divergence of outgoing light rays integrated over $S_s$ under
change of section to geometric (convexity and curvature) properties of $S_s$
and the energy-momentum content of the space-time. We derive this formula using
the Sparling-Nester-Witten identity for spinor fields on the hypersurface by
appropriate choice of the spinor fields. We discuss several special cases which
have been discussed in the literature before, most notably the Bondi mass loss
formula.
