  We give a surface integral derivation of the leading-order evolution
equations for the spin and energy of a relativistic body interacting with other
bodies in the post-Newtonian expansion scheme. The bodies can be arbitrarily
shaped and can be strongly self-gravitating. The effects of all mass and
current multipoles are taken into account. As part of the computation one of
the 2PN potentials parametrizing the metric is obtained. The formulae obtained
here for spin and energy evolution coincide with those obtained by Damour,
Soffel and Xu for the case of weakly self-gravitating bodies. By combining an
Einstein-Infeld-Hoffman-type surface integral approach with multipolar
expansions we extend the domain of validity of these evolution equations to a
wide class of strongly self-gravitating bodies. This paper completes in a
self-contained way a previous work by Racine and Flanagan on translational
equations of motion for compact objects.
