A Topological and Metric Formulation for the Mechanism of the End of Our Universe and the Cosmic Transformation According to Al-Amr Theory via Mathematical and Tensor Formulation of the Big Cosmic Rotation

This research presents an advanced topological and metric formulation for the end mechanism of our universe and the cosmic transformation within the framework of "Al-Amr Theory", through the mathematical and tensor modeling and formulation of "The Big Cosmic Rotation".The work aims to reveal the crucial dynamical function performed by the Barzakh flow tensor 𝜣𝝁𝝂 as a Phase Transition Operator at the edge of spacetime when the cosmic curvature reaches its critical minimal value 𝑹 ⟶ 𝟎.In this study, we present the complete mathematical derivation of the Jacobian transformation matrix 𝐉𝜷 𝜶 for the operator with a rotation angle of 1800 ( 𝝅 𝒓𝒂𝒅) around the Barzakh non-spacetime gap (the non-spacetime gap).