Gravitoelectromagnetism and stellar orbits in galaxies
  Beyond the Newtonian approximation, gravitational fields in general
relativity can be described using a formalism known as gravitoelectromagnetism.
In this formalism a vector potential, the gravitomagnetic potential, arises as
a result of moving masses, in strong analogy with the magnetic force due to
moving charges in Maxwell's theory. Gravitomagnetism can affect orbits in the
gravitational field of a massive, rotating body. This raises the possibility
that gravitomagnetism may serve as the dominant physics behind the anomalous
rotation curves of spiral galaxies, eliminating the need for dark matter. In
this essay, we methodically work out the magnitude of the gravitomagnetic
equivalent of the Lorentz force and apply the result to the Milky Way. We find
that the resulting contribution is too small to produce an observable effect on
these orbits. We also investigate the impact of cosmological boundary
conditions on the result and find that these, too, are negligible.
