Saving Penrose's trapped surfaces when quantum fields break the rules

Penrose's trapped surface—a region where inward-pointing light rays converge on both sides—anchors the singularity theorem and the weak cosmic censorship conjecture, but both rely on the null convergence condition. Semiclassical gravity, where quantum fields inhabit curved spacetime, routinely violates that condition. By relaxing the definition to a 'sufficiently trapped surface' compatible with averaged or quantum energy inequalities, the new framework recovers geodesic incompleteness and area-theorem results without assuming classical energy conditions. The work extends the geometric foundations of black hole physics into the semiclassical regime.