There are many hypothesis saying that there will a collision between
the milky way and Andromeda galaxy...so what happens when two black
holes will collide??
There's a few answers in the links in my comment above copied, here and here, but it's such a fun question I thought I'd answer it anyway.
With Andromeda and the Milky way's super-massive black holes in their respective centers, those objects are so massive, they are likely to be largely unaffected by any stars in their path and they will just fly towards each other at whatever rate and direction gravity dictates and by the time they get fairly close to each other, their respective gravity should have them moving quite fast towards one another. I don't know if anyone knows if they will orbit around each other for an extended period of time or spiral in fairly quickly. That will depend on the angle of approach. It's possible they could pass by each other, miss and each could get sent far out away from the other, part of an enormous orbit around each other, taking perhaps billions of years to lead to an eventual collision.
There's a few simulated videos out there on what happens when 2 super massive black holes spiral into each other. Here's one.
As Super-Massive black holes approach, each will pass through roughly half of the other galaxy, disrupting the orbits of any stars they pass hear-by, though they'd likely need to pass within less than a light year to have significant effects on the star's direction, which wouldn't happen that often, but it would happen.
Sagittarius A is huge for a black hole, but quite small compared to the space between stars. It's estimated to be about 44 million KM in diameter, which means it would fit (Just barely) inside the orbit of Mercury and our Sun. Mostly it will fly past stars. Andromeda's super massive black hole may be several times larger, but still fairly small compared to the distance between stars it's likely to pass on the way towards their mutual collision.
It's possible that one or both stars will pass through each other's galaxy relatively collision free but it's possible that one or both of them will get close enough to a star to generate a large accretion disk. While black holes don't have charge, their accretion disks do, and if that happens, that could be an interesting and not very well understood interaction between the 2 super-massive objects and their accretion disks. Also, as they spiral in towards each other, several of their near-by stars will be cast any-which way, some of them, inevitably inside towards one of the 2 black holes. It could be a very impressive show.
Finally, as they merge, which, might take quite a bit of time if they end up orbiting each other, perhaps millions, even billions of years. If/when they do merge, there could be some curious and not very well understood gravitational wave effects. bending and stretching of space like ripples. (Gravity already bends space, but not in measurable ripples. Our observation's of gravity warped space is a smooth curve.
I'll re-post this article here from comments that says it's possible for 2 black holes to repel each other if they bend space in opposite spin-directions and approach each other on a level plane. Less close and they could still easily disrupt outer planet orbits, casting some planets every which way.
And how will it effect the other objects revolving around them??
Imagine jellybeans in a salad spinner going as fast as you can spin it, and you remove the top. That's basically what will happen to any near-by stars. Both galaxy centers are quite crowded with stars (and perhaps several black holes) orbiting their centers. The gravity assists from 2 super-massive objects moving towards each other will be significant and, basically stars will be flying all over the place. Stars have tiny masses compared to those objects and they could be sent in any direction.
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