The newtonian model itself doesn't produce this behaviour as it is continuous, so however much bodies accelerate towards each other they can decelerate just as

The newtonian model itself doesn't produce this behaviour as it is continuous, so however much bodies accelerate towards each other they can decelerate just as much once they have passed. In n-body simulation the continuous model is 'squeezed' into time-slices, where bodies can accelerate towards each other in one time-slice and in the next be too far past each other to slow each other down again. Seemingly in the real astrophysical world, blackholes will free-fall towards each other by their masses 'dragging' on spacetime, causing deep perturbations in spacetime (as gravity waves). Eventually there is a 'merge' as you called it, an operation during which the resulting merged body can get a directed kick from the persisting spacetime perturbations, one powerful enough to eject it from a galaxy. In the real world, overall it is expected energy and momentum is not defied during this merge operation, it seems remarkable considering how exceptional and energetic these events appear. edit ...on second thoughts, this 'merge event' produces GRAVITATIONAL PROPULSION - sorry for the caps but I think they might be justified.