  We show that the recipe for computing the expansions $\theta_\ell$ and
$\theta_n$ of outgoing and ingoing null geodesics normal to a surface admits a
covariance group with nonconstant scalar $\kappa(x)$, corresponding to the
mapping $\theta_\ell \to \kappa \theta_\ell$, $\theta_n \to \kappa^{-1}
\theta_n$. Under this mapping, the product $\theta_\ell \theta_n$ is invariant,
and thus the marginal surface computed from the vanishing of $\theta_\ell$,
which is used to define the apparent horizon, is invariant. This covariance
group naturally appears in comparing the expansions computed with different
choices of coordinate system.
