Persistence of spherical trapping
= Persistence of spherical trapping
In a regular double-null region satisfying the <null energy condition>, an initially negative $r_{,U}$ on a <Cauchy hypersurface> remains negative in its <future domain of dependence>. If both spherical <null expansions> are negative at one sphere, the exchanged-coordinate focusing inequality preserves the other sign along its future outgoing null direction. Every later sphere that still exists there remains a <trapped surface>.