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Aron Wall uses the generalised second law of thermodynamics to prove a quantum singularity theorem, extending the idea of a trapped surface to quantum situations. Like Penrose's theorem, it implies null geodesic incompleteness inside black holes and in the past of spatially infinite Friedmann-Robertson-Walker cosmologies. If space is finite, the past can hold only finitely many entropy-producing processes unless the arrow of time reverses. In asymptotically flat spacetime the law also forbids traversable wormholes, negative masses, faster-than-light travel between asymptotic regions and closed timelike curves. Because the semiclassical approximation is used only at low curvature, the results may hold in full quantum gravity.

The Generalized Second Law implies a Quantum Singularity Theorem