Do black holes move through space? I know it was already asked here:
Does a black hole move through space? What happens to other things around it? 
And it might be a very stupid question, but here it is:
From a relativistic perspective, do black holes move through space, or is it the space around them that is curved in such a way that for us they seem to move?
I know there is no absolute frame of reference in relativity, but let's say the standpoint of one blackhole, I would think time is frozen, so without time how can things move?
 A: Yes, they can move through space. LIGO has detected gravitational waves from multiple pairs of black holes orbiting each other, spiraling together, and merging.
A: Consider a black hole with lots of stuff in orbit around it. For example, most galaxies are like this (they have a big black hole at the centre, or, at least, there are good reasons to think that this is so). When all the orbiting stuff moves along together (while still orbiting), surely it makes sense to say the black hole is itself moving along too. For example, eventually one galaxy could bump into another. Indeed, this has happened many times, and with a big telescope we can see some such mergers ongoing now (or rather, at the moment the light set off towards our telescope). 
A: Yes. Here is a geometric perspective. 
Take e.g. the Schwarzschild metric in coordinates $x^\mu=(t,r,\phi,\theta)$:
$$
g_{\mu\nu}dx^\mu dx^\nu=-(1-r_S/r) dt^2 + (1-r_S/r)^{-1}dr^2 + r^2 (d\theta^2+ \sin^2\theta d\phi^2) \qquad \text{(Schwarzschild)}
$$
where $r_S$ is the Schwarzschild radius. The geometry as $r\to +\infty$ will look like Minkowski space in spherical coordinates (for the spacelike part):
$$
g_{\mu\nu}dx^\mu dx^\nu=- dt^2 +dr^2 + r^2 (d\theta^2+ \sin^2\theta d\phi^2) \qquad \text{(Minkowski)}\,.
$$
Consider changing to Cartesian coordinates $(r,\phi,\theta)\to(x,y,z)$, doing a boost (say along the $x$ direction), and changing back to spherical coordinates. The Minkowski geometry will look exactly the same.
However, doing the same for the Schwarzschild geometry will give you a different geometry! (Which I will not write down...) The new geometry corresponds to a boosted Schwarzschild black hole, one which moves at constant velocity relative to the distant observer at $r\to \infty$.
In fact, the same argument tells you that any asymptotically flat black hole can move relative to an observer far away from the black hole. (Of course they don't all have to move at constant speeds; it's just that one can construct constantly moving black hole geometries from the immobile ones by the above argument without actually calculating anything.)
A: Yes they can. Everything moves in space. If you're looking for proof they can move, the Standard Model says the galaxies (which have black holes) are moving away from us. That’s a lot of black holes moving. 
