Can a black hole be destroyed?

I'm going to jump in and perhaps contiversially answer this one.

Yes.

They cannot be destroyed in the traditional sense, ie blown apart, melted, frozen or even annihilated with antimatter but they can 'die' and, indeed, must all eventually disappear. Black holes were once thought to emit nothing of any kind, hence the 'black' part of black holes but, recently, this has been proven false. To completely understand how, a little background on the vacuum of space is needed.

Like the black hole, recent theories have changed how we look at the vacuum. It is no longer considered a void of nothingness, it is a sea of particles that spring into existence in negative and positive pairs, exist for a tiny fraction of a second, then annihilate one another. They are called virtual particles and, despite throwing the nature of the universe almost on its head (and just about breaking the first law of thermodynamics), they have been proven to exist and are now a part of mainstream quantum physics.

Now, these particles exist as pairs of one positive energy particle, and one negative energy particle. They pop in, are attracted to each other, meet and annihiate. And everyone is happy; they could just about be ignored. But when they come into being near a black hole, it can grab the negative particle before it can destroy itself, pulling it into the event horizon from which there is no escape. The positive particle, counting its blessings and graduating from virtual particle to real particle, escapes the black hole as part of what we call Hawking radiation. And it gives the 'black' hole a healthy little glow.

But the negative particle isn't so lucky. the process is extremely complitcated but, with its partner gone and its destruction inside the black hole inevitable, the negative particle also becomes 'real' in a sense. And that sense is its ability to act upon the universe, specifically the black hole. Though there is virtually nothing that can affect a black hole, except to make it larger, the negative energy particle can and it strikes the singularity, disappearing and taking a tiny amount of energy with it.

In large black holes, this process is next to negligable. It would take far longer than the lifetime of the universe to destroy even a small black hole. But for the micro ones, this process can be much quicker, and if they can't find a constant stream of matter to replenish their lost energy they will quickly shrink and evaporate. Even in the large ones their fate is sealed; though it will take incredible peroids of time all black holes are destined to evaporate in this manner.

That is why I said it was possible to destroy a black hole. The trick is not to attack it, but rather to ignore it. You cant kill a black hole by shoving stuff in, you'lll just make it larger and stronger. But you can destroy a black hole by starving it and, if it was possible to artificially produce these negative energy particles, they might be an effective weapon against an object that was, until recently, thought impervious.

There is no known way to destroy a black hole.

Stephen Hawking beleives that Black holes will "evaporate" over time, losing mass until there is not enough gravity to maintain the black hole.