= Isotropic-to-areal weak-field radius change
{title2=$r=\rho+GM+O(G^2M^2/\rho)$}
The area of a symmetry sphere in the weak-field isotropic metric is $4\pi\rho^2(1+2GM/\rho)$. Equating it to $4\pi r^2$ defines the <areal radius> and gives the displayed change. To first order $dr=d\rho$, and replacing $1/\rho$ by $1/r$ changes the perturbation only at second order. This explains why the isotropic angular correction disappears in the <linearized Schwarzschild metric> without discarding spatial curvature.
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