  Some of the dark matter in the Universe is made up of massive neutrinos.
Their impact on the formation of large scale structure can be used to determine
their absolute mass scale from cosmology, but to this end accurate numerical
simulations have to be developed. Due to their relativistic nature, neutrinos
pose additional challenges when one tries to include them in N-body simulations
that are traditionally based on Newtonian physics. Here we present the first
numerical study of massive neutrinos that uses a fully relativistic approach.
Our N-body code, gevolution, is based on a weak-field formulation of general
relativity that naturally provides a self-consistent framework for relativistic
particle species. This allows us to model neutrinos from first principles,
without invoking any ad-hoc recipes. Our simulation suite comprises some of the
largest neutrino simulations performed to date. We study the effect of massive
neutrinos on the nonlinear power spectra and the halo mass function, focusing
on the interesting mass range between 0.06 eV and 0.3 eV and including a case
for an inverted mass hierarchy.
