Logarithmic and Hyperbolic Structures in Mathematics and ‎Their Conceptual Analogies in Physics

2026-06-05T00:49:08+00:00

The inverse function occupies a special position in elementary calculus because the standard power-law rule for integration ‎fails for a particular exponent. This exceptional behavior motivates a broader investigation into the mathematical structure of ‎logarithmic and hyperbolic functions. In this article we examine the asymptotic behavior of logarithmic and inverse functions, ‎with particular emphasis on singularities, asymptotes, and intersection structure. We investigate how logarithmic behavior ‎naturally emerges from inverse power relationships and discuss the geometric significance of the transition between these two ‎classes of functions. The discussion is then extended toward conceptual analogies in physics, especially in relation to ‎asymptotic behavior appearing in special relativity and gravitational theory. Rather than proposing modifications to ‎established physical theories, the article explores mathematical parallels between divergent structures, limiting processes, and ‎physical interpretation.‎ The aim of this work is therefore not to replace existing physical theories, but to highlight mathematical patterns that recur in ‎both analysis and theoretical physics.‎

Applications of Absolutivity Theory: Black Holes, Hawking ‎Radiation, 4D Harmonics Wave Theory, and the Mass-‎Gravity Property

2026-06-05T01:00:16+00:00

Absolutivity theory introduces an objective reality of time within a true four-dimensional spacetime model built on universal ‎simultaneity and an expanding three-dimensional space continuum. The theory unifies asymptotic modified Newtonian ‎gravity with quantum theory within an orthogonal four-dimensional framework that opposes intrinsic spacetime curvature ‎and eliminates gravitational singularities. This paper presents three physical applications of Absolutivity theory: black holes ‎and Hawking radiation, four-dimensional harmonics wave theory, and the mass-gravity property. For black holes and ‎Hawking radiation, Absolutivity predicts a hidden vacuum area located between the massive core and the Schwarzschild ‎radius. Within this region, both photons and mass particles can orbit according to Lagrange's principle of stationary action. ‎Photons experience curvature in a gravitational field without requiring an attractive force, as they possess no mass-gravity ‎property. The theory supports the existence of Hawking radiation from a classical continuum perspective but does not predict ‎complete evaporation of the black hole core. In four-dimensional harmonics wave theory, the true spacetime topology allows ‎energy to ingress from three independent spatial directions toward a single spacetime point. This yields a theoretical energy ‎concentration higher by a factor of the square root of three compared to the one-dimensional Mizohata-Takeuchi conjecture. ‎The treatment emphasizes that dimensional density of energy must be properly accounted for in harmonic analysis. ‎Regarding the mass-gravity property, the gravitational potential field of a particle is shown to be velocity-dependent. As a ‎particle approaches the speed of light, its gravity field becomes confined within the particle structure and cannot radiate ‎outward. Consequently, measurements of gravitational potential fields cannot provide an accurate estimate of the total mass ‎present in the universe. These applications demonstrate that Absolutivity offers a deterministic, causality-embedded, non-‎curved spacetime framework capable of addressing both quantum and astrophysical phenomena.‎

Hyperscience International Journal

Logarithmic and Hyperbolic Structures in Mathematics and ‎Their Conceptual Analogies in Physics

Applications of Absolutivity Theory: Black Holes, Hawking ‎Radiation, 4D Harmonics Wave Theory, and the Mass-‎Gravity Property