# Khronometric theories of modified Newtonian dynamics

## TL;DR

This paper analyzes a relativistic theory of modified Newtonian dynamics (MOND) involving a khronon field, demonstrating its stability in slow motion and its impact on non-stationary systems.

## Contribution

It establishes the non-relativistic limit of the khronometric MOND theory and examines the stability of stationary solutions and corrections in non-stationary regimes.

## Key findings

- The theory has a consistent slow motion limit reproducing MOND solutions.
- Stationary solutions are stable under khronon perturbations in low acceleration regimes.
- Non-stationary systems experience order unity corrections from the khronon field.

## Abstract

In 2011 Blanchet and Marsat suggested a fully relativistic version of Milgrom's modified Newtonian dynamics (MOND) in which the dynamical degrees of freedom consist of the spacetime metric and a foliation of spacetime, the khronon field. This theory is simpler than the alternative relativsitic formulations. We show that the theory has a consistent non-relativistic or slow motion limit. Blanchet and Marsat showed that in the slow motion limit the theory reproduces stationary solutions of modified Newtonian dynamics. We show that these solutions are stable to khronon perturbations in the low acceleration regime, for the cases of spherical, cylindrical and planar symmetry. For non-stationary systems in the low acceleration regime we show that the khronon field generally gives an order unity correction to the modified Newtonian dynamics.