Is there anything known which could destabilize a black hole ?

well, in 100 million years we can see what happens when the 2 in the center of our universe meet.

I don't think it could be destroyed within our 4 dimensions.

The only process that has been proposed that has any theoretical basis is Hawking radiation. This takes an immense amount of time for any reasonable size black hole, however. It might be possible to do something if the black hole is spinning since it is possible to use such things as power sources, which would have to decrease the mass of the BH at least some.

High speed merging with other black holes would only merge the event horizons, not destabilize them. The 'vibration caused by infalling matter' is somewhat related to Hawking radiation, although not identical. The problem is how to break down that event horizon.

Basic Physics still Apply to Singularities.

Add Matter to Matter and you get a Greater Gravity well, Just like Planets or Stars Colliding, with appropriately Scaled Gravitic effects.

Exotic Matter would have to be of Enough Mass to Effect the Considerable Grouping of Mass already there in order to have any Effects Noticeable. The Negative Mass would Mathematically cancel the Gravitic effects Locally(though, Remember, Nature abhors a Vacuum, and would reach Equilibrium in Nanoseconds). Some of the Calculations I've seen as to "Why Black Holes can't lead to another Dimension" would Fall apart at a 0 Mass point....Could sufficient Exotic Matter be the Key, in a Singularity Gate?

About... 6 years ago? Longer? They detected what was believed to be the 2nd largest explosion ever - next to the Big Bang - and they attributed that to the merging of 2 black holes.

By it's very nature, it can't be 'de-stabilized' - it can only grow. Figure, most black holes are at least as massive as the sun, and the most massive object they can come in contact with is another black hole, which, as we've seen - tend to merge into a larger black hole.

One of the most intriguing possibilities is the rupturing of the event horizon - where the border of our universe and virtual unreality would actually fluctuate, giving off emense 'gravity waves' in the local area. In that immediate vicinity, you'd get some very weird time effects, and releases of huge amounts of energy - all when two black holes spiral into each other.

Great idea for a sci fi story. Black hole on a collision course with an exploding galaxy of equal matter. Loud thundering magnetic storm begins to rapidly pulsate. Flashes of prismatic bright light shoot out like sunspots. The whole process is breathtakingly unstable. The end result is a giant ball of gas the volume of the black hole and exploding galaxy combined with a heavy molten core. When this great ball cools it becomes a super-nova-multi-celestial anomaly where upon the largest and heaviest weird creatures arise.

As far as I know the only way to get rid of a black hole is by evaporation through Hawking radiation at it's event horizon. This process takes billions of years for very small black holes and it's not clear what would happen as they last of it evaporated as that would seem to violate thermodynamics as a loss of information. I do know that black hole mergers are well simulated and are not believed to be destabilizing events. In short, I don't know of anything that would destabilize a stellar mass or larger black hole.

This was an important research topic in General Relativity back in the 1970's. The conclusion, as I recall, is a theorem (by Penrose?) that (within the context of classical GR) the area of an event horizon can never decrease, no matter what you do to it. This, of course, does not include quantum effects or the possibility of some kind of substance that somehow makes a negative contribution to the stress-energy.

There are simulation models on the net that display interactions among singularities. Most observations reveal gravity 'objects' formed by specific processes or in specific locations. It may be impossible to frame this question realistically due to the nature of the beast and time allotted to gather data.

Black Holes are the vacuum cleaners of outer space and are the last part of the Big Bang, there are enough of them to cause the Big Crunch...This process happens over and over, like your heart beats.

Rosie O'Donnell

You are right. It's pretty unimaginable to me. A "Black Hole" is black from a knowledge standpoint as well. So many hypotheses about them, which are whimsical mathematics with a little logic and absolutely no factual observation or measurement.