  An Einstein nilradical is a nilpotent Lie algebra, which can be the
nilradical of a metric Einstein solvable Lie algebra. The classification of
Riemannian Einstein solvmanifolds (possibly, of all noncompact homogeneous
Einstein spaces) can be reduced to determining, which nilpotent Lie algebras
are Einstein nilradicals and to finding, for every Einstein nilradical, its
Einstein metric solvable extension. For every nilpotent Lie algebra, we
construct an (essentially unique) derivation, the pre-Einstein derivation, the
solvable extension by which may carry an Einstein inner product. Using the
pre-Einstein derivation, we then give a variational characterization of
Einstein nilradicals. As an application, we prove an easy-to-check convex
geometry condition for a nilpotent Lie algebra with a nice basis to be an
Einstein nilradical and also show that a typical two-step nilpotent Lie algebra
is an Einstein nilradical.
