Will the Sagittarius A* Black Hole eventually swallow the entire Galaxy?

Question

In one of his interviews, Sir Roger Penrose mentioned that when the Milky Way and the Andromeda galaxies eventually "collide" and merge into one, their super-massive black holes will also eventually merge. He further mentioned that the newly formed super-massive blackhole at the centre of the new galaxy will eventually "hoover out" all matter within the galaxy.

I recall reading that this is generally the case with super-massive black holes at the centers of galaxies: they will eventually "eat out" all matter within their galaxies.

Question: why don't the stars and other objects within the galaxies just keep rotating around these black-holes, like they do now? Why will they eventually be swallowed by the black hole's gravity pull?

Answer 1

Black holes do not suck in matter any more than stars and planets do: an object in orbit would remain in stable orbit if nothing perturbed it.

However, in the long run ($10^{19}$ years and more) interactions between stars will perturb their orbits, making many of them end up in the central black hole. An easy way of seeing this is to consider a random close encounter between two stars. They will change velocities, and potentially one will get a sufficiently high velocity to escape the galaxy - but the other one, by energy conservation, would be more tightly bound and orbit in a closer orbit. Eventually the galaxy "evaporates" through this kind of interaction, with heavier stars congregating near and eventually into the black hole and the lighter stars mostly expelled. (For all the mathematical details of this and related processes, see Binney & Tremaine's Galactic Dynamics).

Even if this did not happen, gravitational radiation makes a star orbiting something slowly lose angular momentum and spiral in, but this takes a far longer timescale.

Hence stars either fall in or are expelled over very long timescales.