  An effective energy tensor for gravitational radiation is identified for
uniformly expanding flows of the Hawking mass-energy. It appears in an energy
conservation law expressing the change in mass due to the energy densities of
matter and gravitational radiation, with respect to a Killing-like vector
encoding a preferred flow of time outside a black hole. In a spin-coefficient
formulation, the components of the effective energy tensor can be understood as
the energy densities of ingoing and outgoing, transverse and longitudinal
gravitational radiation. By anchoring the flow to the trapping horizon of a
black hole in a given sequence of spatial hypersurfaces, there is a locally
unique flow and a measure of gravitational radiation in the strong-field
regime.
