  Using Effective Field Theory (EFT) methods, we compute the effects of horizon
dissipation on the gravitational interactions of relativistic binary black hole
systems. We assume that the dynamics is perturbative, i.e it admits an
expansion in powers of Newton's constant (post-Minkowskian, or PM,
approximation). As applications, we compute corrections to the scattering angle
in a black hole collision due to dissipative effects to leading PM order, as
well as the post-Newtonian (PN) corrections to the equations of motion of
binary black holes in non-relativistic orbits, which represents the leading
order finite size effect in the equations of motion. The methods developed here
are also applicable to the case of more general compact objects, eg. neutron
stars, where the magnitude of the dissipative effects depends on
non-gravitational physics (e.g, the equation of state for nuclear matter).
