The Case Against The External Field Effect And A Relativistic MOND Theory

A new paper provides a possible explanation for observational evidence of a MOND-like external field effect, without definitively ruling it out. I made a post about the paper that is being re-examined exactly five years ago today.

We examine the claimed observations of a gravitational external field effect (EFE) reported in Chae et al. 

We show that observations suggestive of the EFE can be interpreted without violating Einstein's equivalence principle, namely from known correlations between morphology, environment and dynamics of galaxies. 

While Chae et al's analysis provides a valuable attempt at a clear test of Modified Newtonian Dynamics, an evidently important topic, a re-analysis of the observational data does not permit us to confidently assess the presence of an EFE or to distinguish this interpretation from that proposed in this article.

Corey Sargent, William Clark, Antonia Seifert, Alicia Mand, Emerson Rogers, Adam Lane, Alexandre Deur, Balša Terzić, "On the Evidence for Violation of the Equivalence Principle in Disk Galaxies" arXiv:2511.03839 (November 5, 2025) (published in 8 Particles 65 (2025)).

Another promising MOND related preprint that uses entropy and temperature (which is associated intimately with entropy) to devise a relativistic gravitational theory that reproduced MOND phenomenology was also released today:

We derive a relativistic extension of Modified Newtonian Dynamics (MOND) within the framework of entropic gravity by introducing temperature-dependent corrections to the equipartition law on a holographic screen. 

Starting from a Debye-like modification of the surface degrees of freedom and employing the Unruh relation between acceleration and temperature, we obtain modified Einstein equations in which the geometric sector acquires explicit thermal corrections. Solving these equations for a static, spherically symmetric spacetime in the weak-field, low-temperature regime yields a corrected metric that smoothly approaches Minkowski space at large radii and naturally contains a characteristic acceleration scale.

In the very-low-acceleration regime, the model reproduces MOND-like deviations from Newtonian dynamics while providing a relativistic underpinning for that phenomenology. We confront the theory with rotation-curve data for NGC~3198 and perform a Bayesian parameter inference, comparing our relativistic MOND (RMOND) model with both a baryons-only Newtonian model and a dark-matter halo model. We find that RMOND and the dark-matter model both fit the data significantly better than the baryons-only Newtonian prediction, and that RMOND provides particularly improved agreement at r≳20kpc. These results suggest that temperature-corrected entropic gravity provides a viable relativistic framework for MOND phenomenology, motivating further observational tests, including gravitational lensing and extended galaxy samples.

A. Rostami, K. Rezazadeh, M. Rostampour, "Relativistic MOND Theory from Modified Entropic Gravity" arXiv:2511.05632 (November 7, 2025).