Dark Matter as Fissures in a Tensioned Space–Time Medium

This document develops a single, simple idea: space–time is not an empty stage, but a continuous medium under tension, and everything we call “matter”, “light”, “dark matter” and “dark energy” are different geometric states of this medium. In this framework, the state of the medium is encoded in a tension field Θ\ThetaΘ. When Θ\ThetaΘ is smooth and nearly uniform, its energy behaves like cosmological dark matter and dark energy: one component clusters and drives structure formation, the other acts as an effective cosmological constant. When the medium is strongly deformed at very small scales, it forms nodes of tension: localized, stable configurations that play the role of ordinary matter (baryons, leptons, etc.). When the medium does not fully “break” into a node but partially fails, it forms fissures: extended defects of the tension field that store energy and gravitate like dark matter halos on galactic and cluster scales. Finally, small oscillations of the medium propagate as tension waves, which at low energies are indistinguishable from light and obey Maxwell’s equations on the effective curved background. These four ingredients – diffuse tension, nodes, fissures and light – define a unified dark sector picture. On large scales, the diffuse tension field provides the cosmological dark matter and dark energy required by the CMB and the expansion history. On galactic scales, gravity is described by an effective modified Poisson equation with a universal acceleration scale a0a_0a0, coupled to a fissure density ρfiss\rho_{\text{fiss}}ρfiss that is created and regulated by the local baryonic density and the gravitational acceleration. This combination naturally reproduces MOND-like behaviour (baryonic Tully–Fisher relation, radial acceleration relation) while keeping a genuine dark matter component and avoiding the usual conflicts with clusters. The central claim of this work is not that a complete fundamental theory is already in hand, but that this tension–fissure framework leads to a concrete, falsifiable effective model. The document makes this explicit by deriving a set of testable equations: a modified Poisson equation for the gravitational potential Φ\PhiΦ with an interpolation function μ(g/a0)\mu(g/a_0)μ(g/a0), a reaction–diffusion equation for fissure dark matter ρfiss\rho_{\text{fiss}}ρfiss, driven by baryons and by the local acceleration, and a cosmological sector in which the same tension field Θ\ThetaΘ generates both dark matter–like and dark energy–like behaviour. From there, the theory is confronted – at least qualitatively and semi-quantitatively – with a series of demanding tests: spiral galaxy rotation curves, the baryonic Tully–Fisher relation, the radial acceleration relation, the structure of high- and low-surface-brightness galaxies, dwarf spheroidal dynamics, cluster mass profiles and colliding systems such as the Bullet Cluster. Throughout, the emphasis is on constraints: a single set of global parameters must work across all these regimes, or the framework fails. The goal of this document is therefore twofold: to lay out, in a clear and systematic way, the conceptual structure of a tensioned space–time medium with nodes, fissures and light; to show that this picture leads to well-defined equations and non-trivial predictions that can be confronted with existing and future data on galaxies, clusters and cosmology.