What question did this study set out to answer?

This work aims to challenge the physical legitimacy of black hole singularities and propose an alternative framework within Extended Classical Mechanics.

May 19, 2026Open Access

On the Physical Inadequacy of Singularities and the Unified Frequency-Governed Framework of Extended Classical Mechanics (ECM)

Key Points

This work aims to challenge the physical legitimacy of black hole singularities and propose an alternative framework within Extended Classical Mechanics.
Introduced Mass Definition Mapping to clarify the differences between ECM and classical mechanics.
Outlined a frequency-governed energetic transition model to interpret black hole dynamics.
Established the Planck boundary as a critical limit for physical interpretation.
Argued that black holes, rather than being zero-dimensional singularities, can be viewed as dynamic transformers in a continuous energetic state.
Presented a unified framework that preserves spatial interpretation and addresses the breakdown of classical geometric constructs.
Highlighted the importance of intrinsic frequency in mapping black holes' gravitational effects to their internal processes.

Abstract

Version 1.1 Note: This revision refines the conceptual framework by incorporating Mass Definition Mapping in ECM vs. Classical and Relativistic Mechanics and the Ethical Publication Statement, strengthening the formal interpretive clarity and publication ethics alignment of the work. Description: The classical black-hole singularity remains one of the most mathematically accepted yet physically unresolved constructs in modern theoretical physics. Within General Relativity (GR), the internal core of a black hole is formally represented by the limiting condition r = 0, implying L = 0, d = 0, and therefore V = 0. This raises a foundational physical contradiction: if a black hole is claimed to obey the relativistic mass–energy relation E = Mc², then the associated mass (M) must remain physically meaningful, which ordinarily requires nonzero spatial support. This paper argues that a strictly zero-dimensional singular core cannot be regarded as a legitimate physical object because it forfeits both spatial existence and localized mass meaning. Once the Planck boundary (ℓP = √(ℏG/c³)) is recognized as the lower limit of reliable physical interpretation, the singularity must be understood not as a real object, but as a signal of formal breakdown in the classical geometric framework. To address this inadequacy, the paper introduces an alternative interpretation through Extended Classical Mechanics (ECM). In ECM, sub-Planck collapse does not terminate in geometric divergence, but transforms through a deterministic, frequency-governed energetic transition: ΔPEECM ↔ Mapp ↔ ΔMM ↔ ΔKEECM governed by the intrinsic frequency relation: fsource = fobserved + Δfsource Under this framework, the black hole is reinterpreted not as an inaccessible zero-volume paradox, but as a dynamic energetic transformer whose internal frequency evolution continuously maps to its external gravitational footprint. ECM therefore restores physical continuity, preserves spatial interpretability, and offers a conceptually unified alternative to classical singularity-based black-hole ontology.

On the Physical Inadequacy of Singularities and the Unified Frequency-Governed Framework of Extended Classical Mechanics (ECM)

Key Points

Abstract

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