The precise maximal zero-energy nontrapping predicate

In the Radu NT source setting, a maximal unparametrized null geodesic in $E$ is a nonconstant smooth null geodesic image with its local geodesic parameterizations, taken up to regular reparametrization, which has no proper continuation as an unparametrized geodesic within $E$. Maximality is relative to this open exterior; its maximal affine parameter interval is allowed to have finite endpoints. Affine completeness is not an added hypothesis.

The source NT condition is that no such maximal null geodesic $\gamma$ with zero stationary energy has $\pi (\gamma )$ contained in any compact subset $K\subset Q=E\mathrm{/}\mathbb{R}$. In quantified form: for every maximal zero-energy null geodesic $\gamma$ and every compact $K\subset Q$, some point of $\pi (\gamma )$ lies outside $K$. It excludes whole-geodesic containment, not every geodesic segment in a compact set. It neither excludes ordinary photon trapping at nonzero stationary energy nor requires a particular spacetime coordinate radius to be unbounded. The compact subsets are in the quotient of the open exterior; approaching the horizon or infinity is not trapped compact containment there.

The source geodesic image and continuation relation specify the maximality predicate within $E$. The quotient topology supplies a definite class of compact sets, and the energy lemma makes the orthogonality test independent of a chosen parameter. Negating existence of a containing compact set is exactly the displayed universal condition. This equivalence uses only the negation of set containment, and makes no assertion that every such geodesic has infinite affine length or that every compact segment must leave its initial compact set in a prescribed direction or time. The definition is therefore the precise source condition rather than a stronger two-sided or affine-completeness substitute.