Black Holes Without Singularities: A Conceptual Reinterpretation of Infinity in Gravitation

Abstract

In classical general relativity, gravitational collapse under broad conditions leads to spacetime singularities where curvature invariants formally diverge and the theory ceases to be predictive. These divergences are usually interpreted not as physical infinities, but as indications that the continuum description of space-time has reached its domain of validity. At the same time, several approaches to quantum gravity – such as string-theoretic fuzzball models, loop quantum gravity and Planck stars – suggest that the would-be singularity is replaced by a finite, highly quantum state. This paper proposes a conceptual reinterpretation of black holes that makes this idea explicit: instead of treating singularities as "points of infinite density", we interpret the black hole itself as a magnitude-state of the collapsed mass–energy. In this picture, "infinity" is not a value attained by physical observables, but a domain marker signalling a transition from a classical configuration space to a new state space of black holes. A simple toy framework is introduced in which classical divergences are replaced by a mapping into a finite magnitude-state operator, capturing the total mass–energy while avoiding singular behaviour. The goal is not to provide a full quantum gravity theory, but to offer a mathematically transparent and physically motivated interpretation of how one can treat ∞ in gravitation in an elegant and controlled way. This may serve as a conceptual bridge between classical singularity theorems and modern ideas about black-hole microphysics and information storage.

Citation

Stepan, R. (2025). Black Holes Without Singularities: A Conceptual Reinterpretation of Infinity in Gravitation.
Zenodo. https://doi.org/10.5281/zenodo.17634650
        

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