GravitoMagnetic Force in Modified Newtonian Dynamics
  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.
