Beyond the Paradox of Zero-Volume Singularities: New Paper Announcement

I am pleased to share the formal release of my latest theoretical paper: "On the Physical Inadequacy of Singularities and the Unified Frequency-Governed Framework of Extended Classical Mechanics (ECM)."

For decades, modern physics has accepted the mathematical construct of the black-hole singularity at r = 0. However, this introduces a profound Geometry-Mass Contradiction: If a black hole adheres to the relativistic mass-energy relation E=Mc², how can that mass physically exist if its volume collapses to absolute zero (V = 0)? When volume vanishes, localized density (ρ = M/V) undergoes a division-by-zero catastrophe, stripping the mass parameter of its physical meaning.

Furthermore, once we recognize the Planck length

ℓᴘ = √(ℏG/c³) 

as the definitive lower boundary of reliable physical interpretation, the literal zero-dimensional core falls entirely outside the domain of experimentally grounded physics. The singularity is not a physical object—it is a signal that our classical geometric framework has broken down.

The ECM Resolution: Frequency-Governed Energetic Continuity

Rather than relying on artificial geometric corrections or white-hole bounces, this paper introduces a continuous, deterministic alternative through Extended Classical Mechanics (ECM).

When matter collapses toward the sub-Planck regime, it undergoes a fundamental phase transition governed by the ECM Manifestation Chain:

ΔPEᴇᴄᴍ ↔ Mᵃᵖᵖ ↔ ΔMᴍ ↔ ΔKEᴇᴄᴍ 

 

Key takeaways from the paper:

Dynamic Energy Transformation: Sub-Planck collapse does not terminate in a geometric dead-end. Instead, static rest-mass transitions systematically into latent and kinetic energetic states controlled by intrinsic source frequency deviations (fꜱᴏᴜʀᴄᴇ = fᴏʙꜱᴇʀᴠᴇᴅ + Δfꜱᴏᴜʀᴄᴇ ).

Transparent Gravitational Mapping: The black hole is stripped of its absolute informational barrier. Internal frequency shifts modulate the system's apparent mass (Mᵃᵖᵖ ∝ Δfꜱᴏᴜʀᴄᴇ), which maps directly and continuously into the external universe via its effective gravitational footprint: Mɢ = Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ).

Restoring Material Realism: By replacing geometric abstractions with a frequency-regulated framework, existence, energy, and gravitation remain continuous, scannable, and physically interpretable.

In alignment with the principles of open scholarship, this work is released under a Creative Commons Attribution 4.0 International (CC BY 4.0) license and is freely accessible to the global scientific community.

Read the full paper across open repositories:

Zenodo (CERN Open Science): https://doi.org/10.5281/zenodo.20249678

SSRN Preprint: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6779678

I welcome thoughts, technical critiques, and open discussions from fellow researchers, physicists, and peers on this alternative ontology of compact gravitational systems.