What effect would a singularity have on the fabric of space time? Galaxies are always moving and it seems that there  are SMBHs at the heart of most galaxies. If black holes actually twist up spacetime so much thru infinite density how do we know that after the black hole passes by that spacetime returns back to normal. 


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*What effect would a singularity have on the fabric of space time?

*Could it have a lingering effect in its wake? 

*Or does the fabric of spacetime instantaneously recover as soon as the back hole passes by? 

*Could that lingering effect be dark matter?
 A: Spacetime isn't an object, like some sort of elastic jelly, that galaxies move through churning it up as they go. Spacetime is a mathematical object that we use for calculating observables in relativity. So there isn't any sense in which a singularity twists up spacetime.
The treatment of singularities is quite subtle in relativity. We describe spacetime as a combination of a manifold and a metric, where broadly speaking the manifold is what confers dimensionality and the metric is what defines distances. Singularities are not included in the metric, so in this sense the singularities are not part of our universe at all.
Note also that with one exception (the Big Bang) we expect all singularities to be hidden away behind event horizons so they cannot have any effect on us. This is known as the cosmic censorship hypothesis, and a singularity that wasn't behind a horizon would be a naked singularity.
Finally we should note that a black hole singularity takes an infinite time to form as measured on our clocks. This is one of the reasons for the suggestion that black holes don't really exist.
