Chapter 49: The No-Shrink Theorem: Mature Black Holes Cannot Shrink

Can a black hole lose mass? In orthodox general relativity, the answer was “no” until 1975. Hawking’s celebrated calculation — quantum fields on a curved spacetime background — predicted thermal radiation at a temperature inversely proportional to mass, implying that black holes slowly evaporate and eventually disappear. This prediction created the information paradox: where does the information go when a black hole evaporates? Five decades of effort — from black hole complementarity to firewalls to replica wormholes — have not produced a consensus resolution.

Category τ answers the original question differently. A mature black hole — one that has completed ringdown and achieved torus-vacuum stabilization — cannot lose mass. The proof rests on defect monotonicity: mass decrease would require an increase in defect entropy S_def, violating the Categorical Second Law . This is the No-Shrink Theorem . Hawking’s thermal spectrum is not denied — it exists as a readout of the empirical layer — but it does not correspond to ontic mass loss. The information paradox dissolves: no information is lost because no mass is lost.

This chapter also defines the concept of a permanence hallmark: a structural property that, once acquired, cannot be reversed. The No-Shrink Theorem is the first permanence hallmark. It is also the structural input that Book VI will use to connect black hole dynamics to the emergence of life.