Information Recursion and the Dissolution of the Black Hole Information Paradox

Information Recursion and the Dissolution of the Black Hole Information Paradox applies the recursion structure of Unified Recursion Theory (URT) to gravitational collapse and black hole evaporation. The classical information paradox is shown to arise from assumptions that do not survive under recursion constraints. URT does not modify general relativity or quantum field theory. Instead, it identifies which regions of spacetime can physically support irreversible informational updates.

The key mechanism is the formation of a finite freeze radius, r_f, inside the classical horizon. Beyond this surface, curvature-induced stiffness exceeds local thermal capacity and forces the recursion efficiency lambda to zero. Irreversible updates become inadmissible and the informational state becomes fixed. The interior is no longer dynamic, and no additional entropy or microstate evolution occurs. This produces a finite informational depth rather than a diverging interior.

Hawking radiation remains unchanged in its semiclassical form, but its informational origin is clarified. All entropy-producing updates occur in the recursion-admissible region outside the freeze surface. The interior does not contribute to radiation, and outgoing quanta are never entangled with a dynamically evolving interior state. The evaporation process becomes a consistent transfer of admissible recursion updates rather than a release of hidden interior information.

The dynamical analysis from the ISW (Informational Stiffness Wave) framework further shows that perturbations of the stiffness field are overdamped inside the frozen core and cannot propagate. This seals the interior informationally: no signals enter, no signals exit, and no new distinctions form. The paradoxical link between Hawking radiation and interior evolution is therefore removed. The assumptions required for the paradox never occur under URT recursion.

This work completes the informational interpretation of gravitational collapse within URT and demonstrates that once recursion constraints are applied, the black hole information paradox dissolves without altering the established foundations of semiclassical gravity.

URT PAPER FAMILY

This work forms part of the Unified Recursion Theory (URT) research program, which develops a cross-domain framework for physical evolution based on constrained informational recursion and an energy–entropy proportionality law. Each paper in the series is self-contained, while collectively establishing the theoretical structure across quantum, geometric, biological, cosmological, and particle-level domains.

Related URT works available on Zenodo:

FOUNDATIONAL PAPERS

1. Unified Recursion Theory — Core Framework (URT Core)

DOI: 10.5281/zenodo.17642761
Record: https://zenodo.org/records/17642761

2. Discrete Admissible Regimes in Unified Recursion Theory: Operator Closure, Constraint Topology, and the Necessity of Five Operators

DOI: 10.5281/zenodo.18148192
Record: https://zenodo.org/records/18148193

3. Informational Field Theory in Strong Curvature (IFT-SC)

DOI: 10.5281/zenodo.17850379
Record: https://zenodo.org/records/17850379

4. Dynamical Evolution of the Informational Stiffness Field (ISW Theory)

DOI: 10.5281/zenodo.17860533
Record: https://zenodo.org/records/17860533

RESOLUTION PAPERS (PHYSICAL PARADOXES)

5. Informational Recursion and the Dissolution of the Black Hole Information Paradox

DOI: 10.5281/zenodo.17868662
Record: https://zenodo.org/records/17868662

6. ORM and the Quantum Measurement Problem (ORM)

DOI: 10.5281/zenodo.17881944
Record: https://zenodo.org/records/17881944

BRIDGING / CONSTRAINT PAPER

7. Distinguishability Geometry in Informational State Space

DOI: 10.5281/zenodo.17957062
Record: https://zenodo.org/records/17957062

Provides the geometric foundation for informational state space.
Underpins the emergence of spacetime, efficiency universality, and landscape geometry.

THEORETICAL EXPANSION PAPERS

8. Emergent Spacetime from Informational Recursion

DOI: 10.5281/zenodo.17885555
Record: https://zenodo.org/records/17885555

9. λ-Universality Across Scales (λ-UAS)

DOI: 10.5281/zenodo.17934065
Record: https://zenodo.org/records/17934065

10. Free-Energy Landscape Geometry in Unified Recursion Theory

DOI: 10.5281/zenodo.17940995
Record: https://zenodo.org/records/17940995

BIOLOGY / COMPLEXITY PAPER

11. URT in Biology: Efficiency, Folding Funnels, Replication Fidelity, and Molecular Motor Dynamics

DOI: 10.5281/zenodo.17945209
Record: https://zenodo.org/records/17945209

COSMOLOGICAL EXTENSIONS

12. Cyclic Cosmology from Informational Recursion

DOI: 10.5281/zenodo.17955043
Record: https://zenodo.org/records/17955043

13. Antimatter as Inverse Recursion: Temporal Operator Asymmetry and Matter–Antimatter Imbalance in Unified Recursion Theory

DOI: 10.5281/zenodo.17955043
Record: https://zenodo.org/records/17955625