Emergent Gravity Project

Emergent Gravitational Response from Structural Constraints

Companion site for the current version of the paper by Mário Filipe Dias, highlighting the accumulated structural variable S(r), class-dependent κ(S) relations, and observational structure in galaxy rotation curves.

The paper

This work analyzes SPARC galaxy rotation curves and shows that the inferred compressibility profiles κ(r) do not follow a universal law, but instead organize into a small number of distinct dynamical classes.

A central result is that, when re-expressed in terms of an accumulated structural variable S(r), these profiles become significantly more regular and admit simple class-dependent logistic relations κ(S).

The existence of a transition scale Sc suggests that the dynamical discrepancy may reflect organized structural regimes rather than a single universal correction.

Current version:
emergent_gravity_v15_4.pdf

Project summary

The goal of this work is to explore whether the observed discrepancy between baryonic and dynamical mass in galaxies may encode structured regimes rather than only an additional matter component.

The key result is the emergence of class-dependent κ(S) relations and a characteristic transition scale Sc.

Data and methods

Compressibility:

κ(r) = Vbar²(r) / Vobs²(r)

Structural variable:

S(r) = ∫₀ʳ | d log Vbar / dr′ | dr′
  • SPARC dataset used
  • κ(r) reconstructed for each galaxy
  • Profiles classified into dynamical families
  • Reparametrization using S(r)
  • Class-dependent logistic κ(S) fits
  • Robustness tested under Υ variations

News & Updates

April 2026: v15.4 released — introduction of S(r), κ(S) relations, and robustness analysis.