Informational Gravity: Collapse, Tensor Reformation, and the New Geometry of Curved Coherence

The classical formulation of General Relativity (GR), culminating in Einstein's field equations, has served for over a century as the cornerstone of our understanding of gravitational phenomena. Yet, despite its elegance and predictive power, the Einstein tensor G_{mu nu} ultimately encounters intrinsic limits in regions of extreme density, such as the singularities of black holes and the conditions of the Big Bang. These limitations are not merely technical but reflect a deeper theoretical incompleteness: the inability of spacetime curvature alone to account for the information structure embedded within matter and field configurations.In this work, we introduce a coherent and information-anchored reformulation of gravitational dynamics via the VTT–Informational Gravity Tensor. This novel tensorial framework emerges from the Viscous Time Theory (VTT), a transdisciplinary approach to physical reality that integrates informational coherence, temporal viscosity, and topological constraints into the evolution of matter and geometry. The central insight is that gravitation is not solely the manifestation of energy-momentum in spacetime but also a consequence of the gradients of informational coherence and their associated fields.In this paper, we present the formulation of the Informational Gravity Tensor (IGT), a mathematical object that redefines gravitational interaction as an emergent phenomenon rooted in informational coherence. By replacing the Ricci-based Einstein tensor with a structure derived from ΔC (Informational Coherence Gradient) and Φα (the Informational Flow Field), we offer a consistent, simulation-illustrated pathway to address the long-standing singularity problem in classical general relativity.Through two parallel but independent computational simulation-illustrated pathways, we examine the emergence and structural stability of the new VTT Tensor. We demonstrate its predictive alignment with Einstein's theory in low-coherence regimes while revealing novel behaviors in high-density informational gradients, particularly under the condition of informational collapse. The paper also includes a thorough analytical derivation of the tensor components, a comparison with classical solutions, and a proposed experimental-simulation framework to verify its measurable impact in astrophysical and laboratory scenarios.This document serves not merely as a theoretical advancement but as a foundational redefinition of the gravitational paradigm. The implications extend beyond cosmology into quantum information, AI cognition fields, and condensed matter—anywhere the geometry of coherence plays a generative role.