Black Holes Without Singularities: A Conceptual Reinterpretation of Infinity in Gravitation
Abstract
In general relativity, collapsing matter produces spacetime singularities under very general conditions: curvature invariants diverge, geodesics terminate after finite proper time, and the theory loses its predictive power. These divergences are usually read not as physical infinities, but as a sign that the continuum description of spacetime has reached the boundary of its domain of validity. Various approaches to quantum gravity — such as fuzzball models or Planck stars — accordingly replace the singularity with a finite, strongly quantum-mechanical state.
This paper makes that idea explicit at a conceptual level. A black hole is understood as an absolute-value state of the collapsed mass-energy; "infinity" is not a value that observables take, but a domain marker signaling the transition from the classical configuration space into a new state space of black holes. A simple mathematical framework makes the transition precise: a critical density defines a transition radius below which the configuration is mapped by an absolute-value-state operator onto a finite state. The looming divergence triggers this mapping rather than yielding an infinite value.
The framework does not replace a theory of quantum gravity; it provides a controlled language for handling infinities in gravitational collapse and connects the classical singularity theorems with modern scenarios of singularity resolution.
Citation
Stepan, R. (2025). Black Holes Without Singularities: A Conceptual Reinterpretation of Infinity in Gravitation.
Zenodo. https://doi.org/10.5281/zenodo.17634650