  We present a new approach to studying the evolution of massive black hole
binaries in a stellar environment. By imposing conservation of total energy and
angular momentum in scattering experiments, we find the dissipation forces that
are exerted on the black holes by the stars, and thus obtain the decaying path
of the binary from the classical dynamical friction regime down to subparsec
scales. Our scheme lies between scattering experiments and N-body simulations.
While still resolving collisions between stars and black holes, it is fast
enough and allows to use a large enough number of particles to reach a smooth
and convergent result. We studied both an equal mass and a 10:1 mass ratio
binaries under various initial conditions. We show that while an equal mass
binary stalls at a nearly circular orbit, a runaway growth of eccentricity
occurs in the unequal mass case. This effect reduces the timescale for black
hole coalescence through gravitational radiation to well below the Hubble time,
even in spherical and gasless systems formed by dry mergers.
