Around MOND: Lagrangians, Hubble Equations, Perturbations and External Field Effect

TL;DR

This paper explores a Lorentz-violating Aether theory linked to MOND, deriving its equations, analyzing effects on galaxy models, and highlighting the external field effect that challenges the strong equivalence principle.

Contribution

It introduces a Lorentz-violating Aether Lagrangian linked to MOND and analyzes its implications for galaxy dynamics and the external field effect.

Findings

Aether Lagrangian form studied and derived.

External field effect demonstrated in galaxy models.

Breaks the strong equivalence principle in MOND context.

Abstract

The MOdified Newtonian Dynamics (MOND) is presented here, as well as a theory that can be linked to it: the theory of the Aether, a four-vector field breaking Lorentz invariance. The form of its Lagrangian is studied, then basic equations of the theory are rederived in a detailed way, and calculated for different metrics, exploring the impact of non-zero spatial terms of the Aether. A brief attempt of making the Aether Lagrangian depend on a scalar field is presented. An analytic solving of a galaxy model with an external field is described, which highlights the MONDian external field effect that breaks the strong equivalence principle.