Clarifying the Schwarzschild Singularity: The Principle of Coordinate-Entity Separation and the Ontological Necessity of R_{\min} Ver5
Abstract
Version 5 was initially made public but was subsequently restricted due to identified errors.While this version contains excessive claims and inaccuracies, it is currently undergoing revision.Nevertheless, as the core line of reasoning has remained consistent since Version 1, we have decided to restore Version 5 to public access. The improved and corrected content will be fully integrated into Version 8.To clarify once again, Version 5 is being made available solely on the basis of the consistency of its central argument regarding the distinction between coordinates and physical entities.We openly acknowledge the presence of excessive claims and errors within Version 5. We sincerely apologize for any confusion this may have caused and would be deeply grateful for the readers’ generous understanding.From this perspective, although the underlying argument remains consistent, Versions 2 through 4—which contain similar types of errors—will remain restricted. ======== To enhance the persuasive power of the theory, I have intentionally employed a relatively strong tone in several places. I kindly ask for the readers’ understanding in this regard. My position has always been consistent. I do not, and will never, claim that my view alone is correct. My sole intention is to engage in dialogue through theory, and I sincerely hope that this work may contribute, even in a small way, to academic discussion. I am fully aware that there remain many aspects in which I am still insufficient to participate in such dialogue at a complete level. Nevertheless, I will continue to make every effort to improve, step by step. I would like to state clearly that this work does not seek to deny or reject existing theories. Although a somewhat strong tone is used in parts, the intention is to explore, based on personal reasoning, possible ways to further complement and refine established theoretical frameworks. I also wish to emphasize that this work is presented as a preprint. It is not a validated or formally verified theory, but rather a theoretical construction developed by an individual with the assistance of AI tools. I would appreciate it if readers would keep this context in mind while reading. Despite multiple rounds of review, errors may still remain. I sincerely ask for the readers’ understanding and generosity in this regard. Thank you for your time and consideration. I hope that everyone who takes the time to read my work finds some measure of fulfillment and well-being in doing so. Sincerely,Sungmin Lee =================== This paper addresses the long-standing problem of curvature divergence at the r \to 0 singularity in the Schwarzschild metric. We identify this singularity as a Reification Fallacy—a logical error where a geometric coordinate origin is conflated with a physical mass-entity. By introducing the Principle of Coordinate-Entity Separation, we demonstrate that while a coordinate address can exist at r=0, any physical mass M with finite energy density must possess a non-zero physical extent, defined here as R_{\min}. Unlike previous "regular black hole" models, this framework preserves the standard Einstein field equations and the Schwarzschild exterior while establishing R_{\min} as the natural ontological boundary of the source. This conceptual shift transforms the black hole interior from a mathematical void into a dynamical physical core. We further propose that the R_{\min} core possesses vibrational degrees of freedom that couple with the event horizon, providing a theoretical foundation for Gravitational Wave (GW) Spectroscopy. This allows the internal structure of black holes to be investigated through GW echoes and quasi-normal mode analysis, turning black holes into researchable physical laboratories.