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The Bondi-Sachs formalism uses outgoing null hypersurfaces to describe gravitational radiation. A null coordinate $u$ labels wavefronts, areal radius $r$ labels cross-sections, and angular coordinates label null generators.

The Einstein field equations split into radial relations and evolution equations for the angular geometry. At future null infinity, changing Bondi shear gives the Bondi news function, linking radiation to loss of Bondi mass in nonlinear general relativity.^[ref]

The Bondi shear is the leading trace-free angular distortion in an asymptotically flat spacetime described by Bondi-Sachs coordinates. In a common expansion, the angular metric is $h_{AB}=q_{AB}+C_{AB}/r+O(r^{-2})$, with $q^{AB}{C}_{AB}=0$.

Its retarded-time derivative determines the Bondi news function, with normalization depending on convention. The distinction matters: a nonzero but time-independent shear need not represent ongoing radiation, while changing shear describes radiative degrees of freedom. Changes between early and late configurations are also connected with gravitational memory.^[ref]

The azimuthal metric component isSince $\gamma =c/r+O(r^{-2})$,Thus the Bondi news function satisfies