  In this work we obtain the limit of the Hawking energy of a large class of
foliations along general null hypersurfaces $\Omega$ satisfying a weak notion
of asymptotic flatness. The foliations are not required to be either geodesic
or approaching large spheres at infinity. The limit is obtained in terms of a
reference background geodesic foliation approaching large spheres and a
positive function, constant along the null generators on $\Omega$, which
describes the relation between the two foliations at infinity. The integrand in
the limit expression has interesting covariance and invariance properties with
respect to change of background foliation. The standard result that the Hawking
energy tends to the Bondi energy under suitable circumstances is recovered in
this framework.
