Authors :
Ibrahim Hassan Hassan Osman
Volume/Issue :
Volume 11 - 2026, Issue 10 - October
DOI :
https://doi.org/10.38124/ijisrt/26Oct946
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Abstract :
This paper presents an extended tensor formulation adhering to the principle of general covariance of Al-Amr theory, through the derivation of t Ibrahim-Einstein field equations. This study aims to formulate the algebraic constants of the theory, represented by Ibrahim constant and the length density of macroscopic universe, within a modified geometricdynamical model of the cosmic action integral .The derived equations are distinguished by the introduction of a new tensor called the Barzakh flux tensor, which is mathematically responsible for quantifying and describing the mechanism of "continuous creation" and the injection of mass and momentum individually across the Barzakh (non-spacetime gap) that connects the two opposite spacetimes: macroscopic and microscopic universe .By applying the extended tensor field equations to the Friedmann-Lemaître-Robertson-Walker (FLRW) metric, we succeeded in deriving modified cosmic expansion equations that explain the accelerated expansion of macroscopic universe as an authentic statistical geometric property, instead of assuming unknown dynamic dark energy fields .The results prove that the geometric value of the developed cosmological constant, constrained by modern astronomical observations from Planck 2018 and + Pantheon catalog, provides a radical and complete solution to the vacuum energy problem consistent with Ibrahim number. Moreover, this tensor formulation provides a physical mechanism to protect the laws of physics from collapse at critical densities, clarifies the reality of the singularity as a unique, unparalleled entity existing beyond our universe, separate from it, at the highest and the most perfect rank of existence, and explains the black hole as a non-spacetime passage separating two opposite spacetimes , which eliminates the need to assume artificial inflationary fields.
Keywords :
Ibrahim-Einstein Field Equations, Barzakh Flux Tensor, Ibrahim Number, Vacuum Energy, Phase Transition, Cosmic Length Density.
References :
- Weinberg, S. (1989). "The cosmological constant problem". Reviews of Modern Physics.
- Ibrahim H. H. O., Osman (2026). "Verification of Al-Amr Theory Constants Using N-Test Results from Planck 2018 and Pantheon+". IJISRT, 11(9).
- Ibrahim H. H. O., Montasir S. T. (2023). "Solving the Problem of the Cosmological Constant and Vacuum Energy Density". IJISRT, 8(2).
- Ibrahim H. H. O., Mubarak D. A. (2022). "Reconciling general relativity with quantum theory". IJISRT, 7(11).
- Ibrahim H.H.O." The End of our Universe by a Sudden Phase Transition at its Present State According to the Created-Built Model ", IJISRT - International Journal of Innovative Science & Research Technology,Vol.8 Issue1, Jan.2023
- Ibrahim H. H. O. (2023). "Verification of Al-amr Principle and Determination of the Maximal Universal Acceleration". IJISRT, 8(3).
- Di Valentino, E., et al. (2021). "In the realm of tension—a review of statistical variances". Classical and Quantum Gravity.
This paper presents an extended tensor formulation adhering to the principle of general covariance of Al-Amr theory, through the derivation of t Ibrahim-Einstein field equations. This study aims to formulate the algebraic constants of the theory, represented by Ibrahim constant and the length density of macroscopic universe, within a modified geometricdynamical model of the cosmic action integral .The derived equations are distinguished by the introduction of a new tensor called the Barzakh flux tensor, which is mathematically responsible for quantifying and describing the mechanism of "continuous creation" and the injection of mass and momentum individually across the Barzakh (non-spacetime gap) that connects the two opposite spacetimes: macroscopic and microscopic universe .By applying the extended tensor field equations to the Friedmann-Lemaître-Robertson-Walker (FLRW) metric, we succeeded in deriving modified cosmic expansion equations that explain the accelerated expansion of macroscopic universe as an authentic statistical geometric property, instead of assuming unknown dynamic dark energy fields .The results prove that the geometric value of the developed cosmological constant, constrained by modern astronomical observations from Planck 2018 and + Pantheon catalog, provides a radical and complete solution to the vacuum energy problem consistent with Ibrahim number. Moreover, this tensor formulation provides a physical mechanism to protect the laws of physics from collapse at critical densities, clarifies the reality of the singularity as a unique, unparalleled entity existing beyond our universe, separate from it, at the highest and the most perfect rank of existence, and explains the black hole as a non-spacetime passage separating two opposite spacetimes , which eliminates the need to assume artificial inflationary fields.
Keywords :
Ibrahim-Einstein Field Equations, Barzakh Flux Tensor, Ibrahim Number, Vacuum Energy, Phase Transition, Cosmic Length Density.
