String Network Gravity: A Structural Approach to Spacetime Deformation and Black Hole Phase Transitions

Abstract

We propose a novel discrete framework for gravitational phenomena based on the concept of string elements — edges of a cubic complex whose connectivity and weights constitute the fundamental structure of space. In this model, gravity is not treated as a force but as a structural deformation of the string network induced by the presence of mass. We demonstrate that extreme gravitational conditions (black holes) correspond to phase transitions in the network topology, replacing the classical singularity with a limiting connectivity regime. The event horizon is reinterpreted as a surface where the network ceases to support outward information pathways, rather than a spatial boundary. We develop the dynamical equations governing network evolution, analyze stationary states and linear stability, and establish formal connections to Regge calculus, graph Ricci flow, spectral graph theory, and percolation theory. The model naturally reproduces the area-scaling of black hole entropy through combinatorial arguments. Numerical consistency checks of the horizon scaling law (linear in mass) and the area law (horizon edge count proportional to the square of the horizon radius) are presented for the screened Poisson limit.

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