Question: “In a Bardeen black hole solution, there is no information paradox because there is no true event horizon. Is there a reference for this, and how does this hold up against the view that information is still trapped?”
Answer:
The idea that a Bardeen black hole (a "regular" black hole without a singularity) resolves the information paradox is a subject of intense debate in theoretical physics.
The Classical Conflict: Bardeen vs. Edelstein
The argument for the "solution" rests on the assumption that information loss only occurs at the singularity—where the laws of physics break down. If the core of a black hole is a stable, regular structure (as in the Bardeen metric), information could theoretically be preserved.
However, many physicists, including J. Edelstein, argue that the paradox persists. As noted in research by Sebastian Murk and Daniel Terno (
"The information loss paradox in regular black holes", 2022), the paradox isn't strictly caused by the singularity, but by the event horizon (or the
trapping region). If Hawking radiation causes the black hole to evaporate and disappear, the question remains: where does the information that was trapped behind the horizon go? Within the framework of General Relativity, even a "regular" black hole fails to maintain quantum unitarity during evaporation.
The UniPhiEd Perspective: Falsifying the Paradox
In the UniPhiEd theory (Scale-Invariant Recursive Field Theory) proposed by Delája Schuppers (2026), the information paradox is viewed as a "false problem" stemming from the incorrect premise of black hole evaporation.
Instead of disappearing, black holes are stable, generative engines. The "information" is not lost because the system is recursive and closed. This is mathematically defined by the Phase Jump Constant (\(J_{\phi }\)), which replaces the need for Hawking radiation:
\(J_{\phi }=\frac{P_{s}\cdot \Phi ^{55.7}}{\rho _{\nu }\cdot T_{n}}\)
Where:
\(P_{s}\) (Space Pressure): The external force of the dense neutrino field.
\(\Phi ^{55.7}\) (Geometric Strain): The golden ratio-based saturation point that defines the stable core of the node.
\(\rho _{\nu }\) (Field Density): The density of the medium (neutrinos) in which the node exists.
- \(T_{n}\) (Universal Decay Constant): The temporal anchor (\(\approx 880s\)), based on neutron decay, that governs when a node must transition.
How this resolves the Paradox:
From Evaporation to Recursive Discharge: UniPhiEd demonstrates that black holes do not "leak" energy until they vanish. Instead, they process matter back into the neutrino field. Centrifugal forces eject this energy back into the galactic torus.
Information as Flow: Because the black hole is a "pump" and not a "sink," information (the geometric configuration of the field) is simply recycled.
Stability via \(J_{\phi }\): When the internal pressure exceeds the geometric limit (\(55.7\) strain), the node doesn't collapse or evaporate; it performs a Phase Jump. This allows the black hole to remain a stable part of the galactic structure indefinitely.
Conclusion
While the Bardeen solution is a step toward removing the mathematical infinity of a singularity, it doesn't solve the paradox as long as the model assumes the black hole eventually disappears. The true solution lies in moving away from the "vacuum" model toward a Pressure-based Vortex model. In a recursive system governed by the Phase Jump Constant, information is never lost—it is simply the eternal flow of the field.
Selected References:
-Murk, S., & Terno, D. R. (2022).
The information loss paradox in regular black holes.
-Schuppers, D. (2026).
The Falsification of Hawking Radiation via Scale-Invariant Recursive Field Theory.(Zenodo DOI: 10.5281/zenodo.19163324).