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Bondi-Sachs coordinates $(u,r,x^A)$ follow outgoing null hypersurfaces. The retarded time $u$ labels the hypersurfaces, the angles $x^A$ label their null generators, and the areal radius $r$ fixes the angular area element. The coordinate conditions include $g_{rr}=g_{rA}=0$ and $\det g_{AB}=r^4\det q_{AB}$, where $q_{AB}$ is the unit-sphere metric.

Flat spacetime already illustrates the construction: setting $u=t-r$ in units $c=1$ gives $d{s}^2=-d{u}^2-2dudr+r^{2}d{\Omega }^2$. Constant-$u$ surfaces are outgoing light cones, although $g_{uu}$ is nonzero. The null condition concerns the hypersurface normal and gives $g^{uu}=0$.^[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]