As a black hole passes through spacetime, does it affect it? Nothing in the universe stands still. It's always on its way from somewhere to somewhere. A black hole follows a trajectory through the universe, moving from one locus in spacetime to another locus.
Deep inside each black hole is a point that we've never been able to characterize.My question is, does the singularity, and possibly the powerful gravitational fields around the singularity have any measurable effect on the area of spacetime it passed through? One imagines an undeformed area of spacetime. After some time, a black hole passes through this spacetime, then moves on. Does the spacetime it passed through simply go back to being everyday, garden variety undeformed spacetime?
No, a black hole, or any other gravitationally attracting object for that matter, does not change spacetime permanently, but only affects spacetime around it. The easiest way to see this, is to view the BH in its own frame of reference. Here, the BH is stationary, and spacetime around it is described by the Schwarzschild metric. If a BH came by you and left a physical imprint on spacetime after it (like a wake), then from the BH's frame that would mean that you would fly by it, and it would start producing a wake in the direction that you moved. You don't have such an effect on BHs.


Wrong scenario of observer and black hole passing each other, as viewed from the observer's (left) and the black hole's (right) reference frames.