Primordial Black Holes as Geometric Textures: Resolving the Dark Matter Mystery in the Zhang Effective Metric

Dark matter remains the central unsolved puzzle of cosmology. Motivated by decades of null detection results for particle dark matter candidates such as WIMPs, this work constructs a primordial black hole (PBH) scenario within the rotational-order geometric unification framework. During an early-universe spontaneous symmetry-breaking transition of the internal S³ orientation field, the Kibble–Zurek mechanism generates non-singular topological textures with non-trivial winding number π₃(S³)=ℤ. Sufficiently overdense textures decouple from the Hubble flow and collapse gravitationally into primordial black holes. The predicted PBH mass range spans from sub-asteroid mass up to stellar mass, controlled by the phase-transition energy scale Λ_geo. This PBH dark matter channel is complementary to the ultralight geometric axion candidate in Paper 53. Both dark matter candidates arise from the same S³ fibre geometry of the Zhang Effective Metric, without requiring new fundamental particles. The spectrum can be tested by microlensing surveys (Roman, Subaru HSC) and next-generation gravitational-wave detectors including LISA and the Einstein Telescope.