Informational Projection Theory II: Black–Hole Horizons, Entropy, and Informational Conservation

Informational Projection Theory (IPT) describes physical reality as the real projection of a complex informational field I = IR + iII on a manifold equipped with an informational measure, a projection map, and a closed curvature relation. In a previous work, “Informational Projection Theory: A Three–Parameter Informational Framework for Quantum, Gauge, and Cosmological Constants” [10 ], a minimal three-parameter informational Lagrangian was shown to reproduce the structure of electromagnetism, an Einstein-like gravitational coupling, a Hilbert-space kinematics, and late-time cosmological and gauge constants without extreme fine tuning. In this second paper we apply the same informational framework to black-hole horizons and the information problem. We develop a quasi-local notion of informational horizon, in which a macroscopic black hole is characterised by a closed curvature configuration G = dII supported near a null hypersurface, together with an open informational field IR that describes Hawking-like radiation in the real projection. The Bekenstein–Hawking area law is reinterpreted as a statement about the fraction of the fixed total informational norm E0 stored in non-projected curvature modes, and a parameter-independent horizon relation 4GN c7 SH κ2 H = πkB ℏ is shown to hold for Schwarzschild black holes, where SH is the horizon entropy and κH the surface gravity. This horizon invariant is the black-hole counterpart of a de Sitter invariant relating the cosmological horizon entropy and Hubble parameter discussed in the first IPT paper, suggesting a unified horizon–cosmology relation. At the dynamical level, we model evaporation as a slow open–closed exchange process governed by the same efficiency parameter η that appears in the cosmological sector. The resulting evolution of open-sector entanglement entropy follows a Page-curve-like behaviour: an initial rise as information is transferred from infalling matter to near-horizon curvature, followed by a decrease as closed informational structure is gradually re-projected into Hawking-like radiation. Within IPT, no fundamental information loss occurs: the apparent nonunitarity in the real projection arises from discarding the closed sector II , while the full complex field I evolves with a conserved norm. In this sense the black-hole information paradox does not arise in IPT; it is a projection artefact. We also introduce a microscopic toy model that combines the IPT evaporation law, the Bekenstein–Hawking entropy, and Page’s theorem on typical entanglement, yielding an explicit Page curve for the radiation entropy and a Page time tP ≈ 0.65 τevap, consistent with the general expectation that the Page time is of order the total evaporation time. We discuss consistency with no-cloning and monogamy of entanglement, the relation between infalling and asymptotic observers, and the compatibility of IPT black-hole spacetimes with standard energy conditions and weak-field tests.