Directional Models and Regularization of Gravitational Singularities

Abstract This document proposes an alternative theoretical framework based on three original directional models — exponential division, directional coherence, and dynamic tori — with the aim of regularizing classical gravitational singularities, such as the central singularity of black holes and the initial singularity of the Big Bang, without resorting to the canonical quantization of gravity. Rather than treating these singularities as irremediable divergences of curvature or energy-momentum, the proposed framework reinterprets them as directional redirections within the geometric phase space. Exponential division provides a local operator capable of absorbing divergences into a bounded exponential phase; directional coherence imposes a global tensorial constraint guaranteeing the continuity of the dominant eigendirections of fields even under extreme curvature; finally, dynamic tori constitute the natural geometric realization of these constraints, preserving a non-zero minimal spatial extension in the vicinity of classical singularities. Together, these three models form a coherent and hierarchical system of geometric and dynamic regularization, whose unified master equation is presented in section 5.