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June 3, 2026Open Access

Variational Diagnostics and Flow-Entropy Synthesis: A Dual-Facet Approach to Essential Singularities and Event Horizon Dynamics

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Authors

AGAbdo Gamal

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Overview

This research introduces a framework that shows permanent dynamic instability in multivariable functions with singularities.

Key Points

  • The aim is to establish the non-existence of limits for multivariable functions with high-order singularities at the origin.
  • Developed a Dynamic Flow Model within a Diagonal Scanning Cube.
  • Superseded traditional epsilon-delta limit formulation with a topological definition.
  • Analyzed the implications of structural substitution in the manifold of the vector field.
  • Demonstrated that high-order singularities result in permanent dynamic instability.
  • Established that the limit cannot be resolved by classical analytical methods.
  • Showed that rotational torques generated by the Curl operator lead to a high path-entropy state.

Cite This Study

Abdo Gamal (2026) studied this question.

synapsesocial.com/papers/6a1fc49adee9eb8c0dce6292https://doi.org/10.5281/zenodo.20400150
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