I understand that a gravity well bends space-time such that, close to it, time passes "slower" than further away. The archtypical example is that if a chronometer were dropped into a black hole, we would observe it to tick slower and slower as it approached the event horizon. Based on this, I have a couple questions... 1. Suppose two black holes were passing close by each other. They will be changing velocity all the time due to each other's gravity, but let's abstract this away, and worry only about time dilation. Would an observer at infinity, stationary relative to the system's center of mass, see them as slowing down as they passed each other? My understanding is that a slowing would be observed. 2. Suppose two black holes are in concentric orbits around a heavier gravity source. Consider the inner one passing by the outer one, as bodies with smaller orbits around their primary are given to do, but let us ignore the perturbations in their orbits. Would their movement past each other be slowed as in the above case? My understanding is that it would. Now for the part that I find weird...would the orbital speed of the inner black hole appear to decrease while they passed each other? Would the orbital speed of the outer black hole appear to increase while they passed each other? These seem strange, but they seem to follow from the above. If I'm making a conceptual error, please point it out to me--many thanks!