Fully relativistic treatment of light neutrinos in $N$-body simulations
  Cosmological $N$-body simulations are typically purely run with particles
using Newtonian equations of motion. However, such simulations can be made
fully consistent with general relativity using a well-defined prescription.
Here, we extend the formalism previously developed for $\Lambda$CDM cosmologies
with massless neutrinos to include the effects of massive, but light neutrinos.
We have implemented the method in two different $N$-body codes, CONCEPT and
PKDGRAV, and demonstrate that they produce consistent results. We furthermore
show that we can recover all appropriate limits, including the full GR solution
in linear perturbation theory at the per mille level of precision.
