MOND as the weak field limit of an extended metric theory of gravity with torsion

TL;DR

This paper develops a covariant extended metric gravity theory incorporating torsion, which reduces to Modified Newtonian Dynamics (MOND) in the weak field limit, aiming to explain galactic dynamics without dark matter.

Contribution

It introduces a fully covariant extended metric theory of gravity with torsion that reproduces MOND behavior in the weak field regime.

Findings

The theory reduces to MOND in the weak field limit.

Inclusion of torsion and matter Lagrangian functions modifies gravity.

Provides a covariant framework for MOND-like phenomenology.

Abstract

In this article we construct a relativistic extended metric theory of gravity, for which its weak field limit reduces to the non-relativistic MOdified Newtonian Dynamics regime of gravity. The theory is fully covariant and the way to achieve this is to introduce torsion in the description of gravity as well as with the addition of a particular function of the matter lagrangian into the gravitational action.