Virial Theorem in Nonlocal Newtonian Gravity

TL;DR

This paper derives a virial theorem within nonlocal Newtonian gravity, suggesting that nonlocality can mimic dark matter effects and predict galaxy sizes based on a universal length scale.

Contribution

It introduces a virial theorem for nonlocal gravity and explores its implications for galaxy sizes and dark matter simulation.

Findings

Galaxy baryonic diameters are predicted to be larger than a universal length scale times the effective dark matter fraction.

Nonlocal gravity can account for dark matter effects in galaxy dynamics.

The basic nonlocality length scale is approximately 3 kpc.

Abstract

Nonlocal gravity is the recent classical nonlocal generalization of Einstein's theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for "isolated" astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy's baryonic diameter---namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time---is predicted to be larger than the effective dark matter fraction times a universal length that is the basic nonlocality length scale of about 3 kpc.