GravitoMagnetic Force in Modified Newtonian Dynamics

TL;DR

This paper introduces the Gauge Vector-Tensor (GVT) theory, extending MOND to include gravitomagnetic effects within a covariant framework, and discusses its observational implications in galactic and solar system contexts.

Contribution

The paper proposes the GVT theory, a covariant extension of MOND incorporating gravitomagnetism, and analyzes its observational distinctions from mbda CDM.

Findings

GVT can match mbda CDM or MOND at galaxy edges.

GVT predicts measurable anomalies in gravitoelectric fields.

Observations inside specific solar system windows can test GVT.

Abstract

We introduce the Gauge Vector-Tensor (GVT) theory by extending the AQUAL's approach to the GravitoElectroMagnetism (GEM) approximation of gravity. GVT is a generally covariant theory of gravity composed of a pseudo Riemannian metric and two U(1) gauge connections that reproduces MOND in the limit of very weak gravitational fields while remains consistent with the Einstein-Hilbert gravity in the limit of strong and Newtonian gravitational fields. GVT also provides a simple framework to study the GEM approximation to gravity. We illustrate that the gravitomagnetic force at the edge of a galaxy can be in accord with either GVT or \Lambda CDM but not both. We also study the physics of the GVT theory around the gravitational saddle point of the Sun and Jupiter system. We notice that the conclusive refusal of the GVT theory demands measuring either both of the gravitoelectric and gravitomagnetic fields inside the Sun-Jupiter MOND window, or the gravitoelectric field inside two different solar GVT MOND windows. The GVT theory, however, will be favored by observing an anomaly in the gravitoelectric field inside a single MOND window.