= Bondi-Sachs coordinates
{c}
<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 $ds^2=-du^2-2\,du\,dr+r^2d\Omega^2$. Constant-$u$ surfaces are outgoing <light> cones, although $g_{uu}$ is nonzero. The null condition concerns the hypersurface normal and gives $g^{uu}=0$.<Bondi-Sachs Formalism by Thomas Mädler and Jeffrey Winicour>[Section 2, coordinates and determinant condition]{ref}
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