Engine Versions
The DMF theory is implemented in a PHP engine operating on SPARC galaxy data. The engine computes rotation curves, splits galaxies into zones (centre, mid, external disc), and exports detailed JSON files for statistical analysis.
DMF Minimal – First Implementation
First working prototype of the minimal DMF model. Single-field DMF with basic coupling to baryonic gravity. Uses a unified radial treatment without explicit inner/outer split. Useful as a historical baseline for the evolution of the theory.
Dark Matter Fissures (DMF) – Project Overview
This project explores an alternative to particle dark matter that keeps General Relativity intact. Instead of adding a new invisible fluid made of particles, we treat space-time itself as a physical fabric under tension. Baryons (stars, gas) act as heavy nodes that stretch this fabric. Under the right conditions, the fabric develops cracks or defects – what I call Dark Matter Fissures (DMF).
These fissures do not replace gravity. They change how the gravitational field is transmitted through the fabric, creating an effective “extra” gravitational component that looks very similar to a dark halo. At the scale of galaxies, the goal is simple and concrete: reproduce the SPARC rotation curves using a geometric response of the fabric, without adding a standard dark matter halo by hand.
In practice, I build an effective model that takes the observed baryonic distributions of each SPARC galaxy and computes:
- the baryonic gravitational field,
- an effective tension of the fabric as a function of radius,
- a susceptibility that tells how many fissures are active at a given tension,
- a smooth radial DMF profile, and a baryonic extinction that turns the DMF off where baryons already explain the data.
The result is a DMF field that I map to a dark fraction using a simple logistic law. With only a few global parameters and one calibration factor per galaxy, the current “simple” version of the DMF engine already reproduces SPARC rotation curves with about 7–8% mean error on the dark fraction of the disc and a correlation close to 0.99.
A more advanced “full” engine, including additional locking and extinction layers, can reach around 3% mean error but at the price of many sharp non-linear transitions. The current development focus is to keep the simple engine as the clean baseline, gradually reintroducing only the physically meaningful refinements and smoothing the transitions, especially in the central parts of galaxies where the observed dark fraction grows very gently.
Core Concepts
1. Space-Time Fabric Under Tension
Space-time is treated as a fabric characterized by a local tension \( T(R) \). This tension depends on:
- Local baryonic gravity \( g_\mathrm{bar}(R) \)
- Surface compactness of the disc and gas
- Radial gradients of baryonic structures
2. Fissures, Nodes and DMF
Fissures (or cracks) in the fabric represent zones where the tension configuration allows an additional effective field contribution. Nodes and collapsed regions are special configurations that can enhance or suppress this DMF contribution depending on the regime of tension.
3. Susceptibility \(\chi(T)\)
The response of the fabric to baryonic tension is encoded in a susceptibility function \(\chi(T)\). It is generally non-monotonic, with:
- A low-tension regime, where the DMF response can grow;
- An intermediate regime with a peak (often modelled with a log-normal “bump”);
- A high-tension plateau, where the DMF contribution saturates or is strongly limited.
4. Effective DMF Field \(S(R)\)
The DMF field is modelled as: \[ S(R) = \chi\big(T(R)\big)\, F(r_n; P_\mathrm{eff})\, L\big(T(R)\big)\, E(R) \]
- \( F(r_n; P_\mathrm{eff}) \): radial profile controlled by effective parameters and node distribution;
- \( L(T) \): “lock” factor depending on tension regimes and environment type (gas-dominated, node-dominated, mixed, etc.);
- \( E(R) \): extinction or modulation factor ensuring consistency between baryonic gravity and the observed acceleration.
Mathematical Structure
In its minimal form, the total gravitational field is written as:
\[ g_\mathrm{tot}(R) = \mu_\mathrm{bar}\big(T(R)\big)\, g_\mathrm{bar}(R) + \mu_\mathrm{env}\big(T(R)\big)\, g_\mathrm{DMF}(R) \]
where:
- \( g_\mathrm{bar}(R) \): baryonic contribution (stars + gas);
- \( g_\mathrm{DMF}(R) \): effective DMF contribution built from fissures and nodes;
- \(\mu_\mathrm{bar}(T)\) and \(\mu_\mathrm{env}(T)\): tension-dependent functions controlling how baryons and DMF couple to the total field.
A limited set of global parameters (e.g. \( a_0, k_\mathrm{DMF}, \beta_\mathrm{gas}, \beta_\mathrm{node}, g_\mathrm{sat}, a_\mathrm{DMF}, a_\mathrm{bar} \)) is calibrated against SPARC rotation curves. Each galaxy can also have a local calibration factor \( K_g \) while a global factor \( K_\mathrm{DMF,global} \) sets the overall DMF level.