&gt; But they will take infinite time to actually merge though.<p>Yes, from the perspective of a distant observer. From the perspective of an observer falling into the BH, time will pass in the usual way, indeed it must.<p>&gt; The closer they get to that event horizon the slower time goes, so they will take longer and longer to orbit.<p>Only from the perspective of a distant observer. This might explain why black holes last as long as they do, from the perspective of a distant observer. For all we know, they all blow up in short order from the perspective of an observer falling into one.