  This paper presents a general-relativistic N-body technique for evolving the
phase space distribution of massive neutrinos in linear perturbation theory.
The method provides a much more accurate sampling of the neutrino phase space
for the HDM initial conditions of N-body simulations in a cold+hot dark matter
universe than previous work. Instead of directly sampling the phase space at
the end of the linear era, we first compute the evolution of the metric
perturbations by numerically integrating the coupled, linearized Einstein,
Boltzmann, and fluid equations for all particle species. We then sample the
phase space shortly after neutrino decoupling at redshift z=10^9 when the
distribution is Fermi-Dirac. To follow the trajectory of each neutrino, we
subsequently integrate the geodesic equations for each neutrino in the
perturbed background spacetime from z=10^9 to z=13.55, using the linearized
metric found in the previous calculation to eliminate discreteness noise. The
positions and momenta resulting from this integration represent a fair sample
of the full neutrino phase space and can be used as HDM initial conditions for
N-body simulations of nonlinear structure evolution in this model. A total of
21 million neutrino particles are used in a 100 Mpc box, with Omega_cdm=0.65,
Omega_hdm=0.30, Omega_baryon=0.05, and Hubble constant H_0=50. We find that
correlations develop in the neutrino densities and momenta which are absent
when only the zeroth-order Fermi-Dirac distribution is considered.
