  The second-order gravitational self-force on a small body is an important
problem for gravitational-wave astronomy of extreme mass-ratio inspirals. We
give a first-principles derivation of a prescription for computing the first
and second perturbed metric and motion of a small body moving through a vacuum
background spacetime. The procedure involves solving for a "regular field" with
a specified (sufficiently smooth) "effective source", and may be applied in any
gauge that produces a sufficiently smooth regular field.
