Chapter 47: Black Hole Birth as Global Topological Event

What is a black hole? In general relativity, a black hole is a region of spacetime from which nothing can escape — bounded by an event horizon and containing (generically) a curvature singularity. The singularity is the theory’s confession of its own breakdown. The information paradox — the apparent loss of quantum information behind the horizon — has driven four decades of debate in theoretical physics.

In Category τ, a black hole is something quite different. It is a global topological event: the emergence of a non-contractible linking class in τ³ when the gravitational tension at a region of the boundary exceeds the maximum spherical capacity. The horizon is not a sphere S² but a torus T² — the same torus that forms the fiber of τ³. There is no interior singularity (the profinite structure prevents divergences). And there is no information paradox: the boundary preserves all data, because the boundary holonomy algebra H_∂[ω] is invertible.

This chapter defines the τ-native black hole, proves the toroidal topology of the horizon, and derives information preservation as a structural corollary.