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 string elements: edges of a cubic complex whose connectivity and weights constitute the fundamental structure of space. Gravitational effects are modelled without reference to force, curvature, or a spacetime manifold, only as a structural deformation of the network induced by load. Network structures termed black holes correspond to phase transitions in network topology, replacing the classical singularity with a limiting connectivity regime. The horizon is a combinatorial boundary where the network ceases to support outward information pathways; this is an autonomous definition, not a reinterpretation of the general-relativistic event horizon. 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 exhibits area-law scaling of network entropy through combinatorial arguments; this is structurally analogous to area-law behaviour in emergent geometric interpretations, but arises from percolation-theoretic properties of the network, not from thermodynamic entropy. Three-dimensional validation. GPU-accelerated simulations on a 64-cubed cubic lattice with 500 independent realisations per parameter point yield an area-law coefficient C = 12.38 +/- 0.06 (R^2 = 0.99997). The proximity to 4-pi is an empirical constraint of the square-lattice calibration, not a derivation of the Bekenstein-Hawking coefficient. The phase transition is robust across dimensions, with the percolation-dominated regime prevailing in the strong-field limit in both 2D and 3D. A systematic scan over 2D lattice types (square, triangular, hexagonal) shows that the coefficient C = N_H / r_c^2 depends on lattice geometry (12.431, 18.850, and 18.533 respectively), while the area law N_H proportional to r_c^2 itself holds universally; the prefactor is geometry-dependent, not a universal constant. We further show that load relaxation corresponds to a topological phase transition in which the horizon shrinks and vanishes, with total network state conserved throughout — a classical form of network state conservation, not a resolution of the quantum black-hole information paradox.

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