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In this work we obtain the limit of the Hawking energy of a large class offoliations along general null hypersurfaces $\Omega$ satisfying a weak notionof asymptotic flatness. The foliations are not required to be either geodesicor approaching large spheres at infinity. The limit is obtained in terms of areference background geodesic foliation approaching large spheres and apositive function, constant along the null generators on $\Omega$, whichdescribes the relation between the two foliations at infinity. The integrand inthe limit expression has interesting covariance and invariance properties withrespect to change of background foliation. The standard result that the Hawkingenergy tends to the Bondi energy under suitable circumstances is recovered inthis framework.

The asymptotic behaviour of the Hawking energy along null asymptotically flat hypersurfaces