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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 acovariance group with nonconstant scalar $\kappa(x)$, corresponding to themapping $\theta_\ell \to \kappa \theta_\ell$, $\theta_n \to \kappa^{-1}\theta_n$. 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 covariancegroup naturally appears in comparing the expansions computed with differentchoices of coordinate system.

Covariance Group for Null Geodesic Expansion Calculations, and its Application to the Apparent Horizon