Gravitoelectromagnetism and stellar orbits in galaxies

TL;DR

This paper explores whether gravitomagnetism could explain galaxy rotation curves without dark matter, but finds its effects are too small to account for observed phenomena.

Contribution

It provides a detailed calculation of gravitomagnetic effects on stellar orbits in galaxies and assesses their significance relative to galaxy rotation anomalies.

Findings

Gravitomagnetic effects are too weak to influence galaxy rotation curves.

Cosmological boundary conditions have negligible impact on gravitomagnetic effects.

The study rules out gravitomagnetism as a primary explanation for galaxy rotation anomalies.

Abstract

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.