wookiemeister said:
In practical terms wouldn’t there be things being slung around by the black holes of galaxys?
Sure. Although that’s a bit different to a plain Newtonian gravity assist, since relativity rules have to be used when calculating trajectories near a BH, for several reasons. Firstly, the velocities involved tend to be high, so SR effects come into play. But more significantly, the gravity is so intense that the Newtonian approximation for gravitational force
(F = Gm1m2/r²) is no longer accurate, so GR must be used to calculate acceleration in terms of spacetime curvature. Also, if the BH is spinning (which is likely) there will be frame dragging (spacetime twisting) to take into account, too.
The upshot of this is that the classic Newtonian trajectories for a small body orbiting a single large body, the conic sections (i.e parabola, circle, ellipse, hyperbola) are not solutions to motion under GR. Elliptic orbits precess rapidly and soon go chaotic. A circular orbit is kind of stable, but even that will decay relatively rapidly due to gravitational radiation.
So virtually anything that approaches a BH will either cross the EH or get flung away, although some stuff does get into temporary orbits, especially if it can lose some kinetic energy by colliding with other matter in the vicinity, i.e. the BH’s accretion disc.
Of course, such collisions can also cause material to be ejected. And material ejected from the accretion disc tends to travel rather rapidly, otherwise it won’t escape, and the stuff trapped in the disc is already moving at relativistic speeds. So any stuff that falls towards a BH with the right vector to miss the hole & the accretion disk will almost certainly be deflected at a fair clip. :)
Some neutron stars are traveling at very high speeds relative to the mean galactic orbital speed in their (current) neighbourhood. One possible explanation for this is that the supernova explosions that give birth to neutron stars tend to be somewhat asymmetrical, so outer bits can get blasted off in one direction while the collapsed core heads in another direction. And if this happens to a star in a binary (or higher multiple) star system, the escaping neutron star could get a massive gravitational slingshot as it passes its companion star.