Separating Overlapping Event Horizons: Theory

[anubodh]

If 2 black holes have event horizons slightly overlapping,can they ever be separated "theoretically" into 2 separate event horizons given we can apply extremely high forces to pull them apart or will it keep stretching and overlapping even if they are pulled apart?

 

[PeterDonis]

If 2 black holes have event horizons slightly overlapping

This doesn't happen. What happens is the 2 black holes merge into one. When that happens there is only one event horizon, not two. There is no such thing as "overlapping event horizons".

given we can apply extremely high forces to pull them apart

How would you "apply g forces" to a black hole?

 

[anubodh]

@PeterDonis I get that after overlapping you get just 1 event horizon but the singularities inside are still separated.So,what i wanted to know was can we apply external forces in opposite directions so that these singularities start separating.I know it's practically not possible but i want to know whether it's theoretically possible or not.

 

[PeterDonis]

the singularities inside are still separated

No, they aren't. The singularities are not places in space; they are instants of time, which are to the future of all other instants inside the horizon. If two black holes merge, then there is only one singularity, not two, because there is only one "inside the horizon".

This is an area where you have to really train yourself to think in terms of spacetime, not space. A single black hole's horizon is not a 2-sphere; it's a 3-cylinder in spacetime, which you can imagine as a cylinder if you suppress one spatial dimension. The singularity is at the future endpoint of the interior of the cylinder.

When two black holes merge, in spacetime, there is really only one horizon, and always was--it's just shaped like a pair of trousers instead of a cylinder. The region where there are two "legs" of the trousers corresponds to the period of time before the holes merged, and the region where there is just one "trunk" of the trousers corresponds to the period of time after they merge. So there is only one "interior" and therefore only one singularity, at the future endpoint of the trunk of the trousers.

can we apply external forces in opposite directions so that these singularities start separating.

No, because there is only one singularity. See above.