I am pleased to announce that my latest research paper, "Curvature Saturation as a Constitutive Response of Spacetime: Regular Black Holes and Information Preservation," is now officially published and available to the public in both English and Japanese.
In this work, I propose a new framework to address the long-standing problem of spacetime singularities. Instead of treating singularities as inevitable points of breakdown in General Relativity, this framework introduces the concept of "curvature saturation."
Key Highlights of the Framework:
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Spacetime as a Physical Medium: The Einstein field equations are interpreted as the "dynamical balance law" of spacetime, while curvature saturation acts as a "constitutive response" that governs how geometry reacts in extreme, high-curvature regimes.
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Resolution of Singularities: By accounting for the finite curvature capacity of spacetime, the theory replaces classical singularities with stable, finite-curvature cores, leading to regular black hole solutions.
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Cold Remnants: The evaporation process of black holes is shown to culminate in stable "cold remnants," providing a natural mechanism for information preservation and reinterpreting the black hole information paradox.
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Observational Pathways: The framework predicts measurable corrections to black hole shadow sizes and gravitational-wave ringdown frequencies, offering a direct pathway for testing the theory with next-generation instruments like the ngEHT and the Einstein Telescope.
My approach has been to extend the success of General Relativity—preserving its precision in weak-field environments—while supplementing it with a constitutive principle that resolves its internal incompleteness at high energies.
This research is intended as a contribution to the ongoing scientific dialogue on the nature of gravity and the structure of spacetime. I invite researchers and those interested in the foundational questions of physics to read, review, and engage with these findings.
One common critique of foundational gravitational theories is the risk of being perceived as purely theoretical speculation. To address this, a significant portion of this research was dedicated to rigorous numerical analysis and cross-verification with observational constraints.
This framework was not developed in isolation; rather, it was refined through extensive iterative testing. We conducted numerical simulations to map the dynamics of spacetime curvature as it approaches the saturation scale, ensuring that the theory remains consistent with established limits of General Relativity in weak-field regimes.
Key aspects of our verification process included:
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Ringdown Analysis: We simulated the gravitational-wave ringdown frequencies of regular black holes to determine potential deviations from classical Kerr geometry. These results provide a concrete benchmark for current and future gravitational-wave observatories like LIGO, Virgo, and KAGRA.
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Shadow Deviation Calculations: We rigorously modeled the photon orbit trajectories in the presence of a finite-curvature core. This allowed us to calculate the predicted shift in black hole shadow radius, providing a clear observational target for the next generation of the Event Horizon Telescope (ngEHT).
This theory is not merely a mathematical alternative to existing models; it is a proposal for a quantifiable, testable evolution of our understanding of gravity. We have treated the curvature-saturation framework as a predictive tool, rigorously subjecting it to the same physical scrutiny we expect of any viable candidate for describing our universe.
[Title] Curvature Saturation as a Constitutive Response of Spacetime: Regular Black Holes and Information Preservation
[Author] Ken Nakashima
[Date of Publication] March 9, 2026
