I've recently read about the last parsec problem, which states that supermassive black holes should not be able to merge within the current age of the universe. Once they reach a distance of about one parsec, there is no more interstellar matter to slow them down, yet relativistic effects (gravity waves) are still too weak to have a major impact.
For Newtonian bodies, such as moons in the solar system, another factor for orbital changes are tidal effects with their planets. These lead to either a decay or a rise in the moons orbit depending on whether it is below or above the geostationary orbit of its host body. These effects can be very pronounced for black holes, which can sometimes rip apart stars.
This brings me to my question: can black holes themselves be affected by tidal effects? I expect the shape of the event horizon to slightly change depending on the surrounding gravitational field, which could count as a deformation. But as this isn't actually shifting matter around, is this doing any mechanical work? Tidal forces also depend on the matter density of the affected object, as they wouldn't have any effects on point masses. Thus, if a black hole was affected by it, I suppose that would leak information about the matter distribution inside the event horizon to an outside observer.
On the other hand, looking at it from the perspective of some particles inside the black holes, they should be affected by the change in potential like any other object passing by a black hole.