Emergent Scalar Field from Interaction Dynamics in Gravitational N-Body Systems

We introduce a theoretical framework in which a scalar field emerges from interaction dynamics in gravitational N-body systems. The model is based on the hypothesis that the intensity of pairwise interactions acts as a source term for an effective scalar field, whose evolution is governed by a second-order dynamical equation. Within this formulation, the field does not represent a fundamental degree of freedom, but rather a collective quantity encoding the dynamical state of the system. We show that the emergent field exhibits nontrivial behavior, including strong correlation with interaction intensity, amplification during close encounters, and persistent oscillatory dynamics after interaction events. Notably, the field responds to variations in inter-particle distances in a manner that suggests sensitivity to impending dynamical instabilities, indicating a potential predictive role in chaotic regimes. The framework naturally extends to large-N systems, where the scalar field develops collective behavior, transitioning from localized excitations to a global dynamical structure. These results suggest that interaction-driven emergent fields may provide an effective description of complex gravitational systems, capturing features not present in standard formulations based solely on pairwise forces. This article is a continuation of the article: "A Global Instability Functional for the N-Body Gravitational Problem." Part II.