A Formal Derivation of Black Hole Phase Transitions: Matter-to-Radiation Conversion and Information Conservation via Spectral Orthogonality

We present a rigorous mathematical framework for a non-singular black hole in- terior. We propose that gravitational collapse induces a phase transition where baryonic matter is converted into a stationary coherent radiation (SCR) state. Uti- lizing the Eddington-Finkelstein coordinate system, we demonstrate that as the ra- dial coordinate approaches the Planck scale, the manifold undergoes dimensional reduction, leading to a nullification of the metric volume element. Information con- servation is established through the mapping of quantum states into an orthogonal frequency basis within an atemporal frame, effectively resolving the black hole in- formation paradox. The resulting energy density provides a natural mechanism for a radiation-dominated cosmological bounce, consistent with the requirements of a cyclic universe.