= Trapping horizon
A trapping horizon is a hypersurface foliated by marginal two-surfaces with one <null expansion> zero and the other nonzero. A future outer trapping horizon has $\theta_+=0$, $\theta_-<0$ and $\mathcal L_{n}\theta_+<0$ for a future ingoing null normal $n$. Unlike an <event horizon>, this is a quasi-local definition. Under the <null energy condition>, a regular future outer horizon is spacelike or null. The ingoing derivative condition distinguishes its outer type from an inner trapping horizon.
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