What Is the Life Span of a Black Hole?

The lifetime of a black hole is proportional to the cube of the black hole’s mass.

Can anyone offer a simple layman’s explanation for Stephen Hawking’s conclusion that black holes explode about 10 billion years after their formation? originally appeared on Quora, the place to gain and share knowledge, empowering people to learn from others and better understand the world. You can follow Quora on Twitter, Facebook, and Google Plus.

Not ten billion years. Closer to 566,236,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years.

Seriously. That is the expected lifetime of a “small”, three solar-mass black hole. Larger black holes last even longer; the lifetime is proportional to the cube of the black hole’s mass.

As to why it happens… Quantum field theory tells us that even in empty space, particle-antiparticle pairs are created and annihilated all the time. However, the total energy of such a particle-antiparticle pair is zero (energy is not created or destroyed, it is strictly conserved) so one of the two particles in the pair must have negative energy. Such a negative energy state is forbidden to exist by the rules of quantum physics, except for a very brief period of time, which explains why such a pair rapidly annihilates and we do not see a shower of particles and antiparticles coming from empty space.

But things are different in a strong gravitational field. The negative energy particle of the pair may fall in the gravitational field and gain energy. If it falls quickly enough, it may gain enough energy to become a “normal”, positive energy particle, the existence of which is no longer forbidden. Meanwhile, its partner, which started its existence with positive energy to begin with, may have enough energy to escape the gravitational field altogether and fly away to infinity.

Such events happen with a computable probability. To a distant observer, these events appear as radiation coming from the black hole. It really isn’t coming from the black hole proper, but from its neighborhood, but the end result is that a positive energy particle escapes to infinity, while its negative energy counterpart is “swallowed” by the black hole. Therefore, the total mass-energy of the black hole decreases.

The smaller the black hole gets, the faster this process takes place, simply because the gradient (rate of change) of the gravitational field near the black hole becomes steeper, making it easier for the negative energy particle to rapidly gain kinetic energy. But it really is not an explosion, except perhaps near the very end. When the black hole decreases in size to less than a billion metric tons, it still has a trillion years to live, but it is already subatomic in size yet emits nearly a gigawatt of power, mostly in the form of gamma radiation. Near the very end, when it only has a year to live, it still weighs over 70 thousand metric tons, but now emits over 6,800 terawatts, something like a thousand times the total power generation capacity of our civilization. By the final second, the power output of this black hole reaches 0.0018% of the power output of the entire Sun. In that final second, some 230 metric tons of mass is converted into radiation. That’s nearly 5 million megatons of TNT equivalent, many thousand times more than the total nuclear arsenal of all nuclear powers combined.

So yes, that’s quite an explosion. But don’t forget that some 18 million years prior to that final second, the black hole would already be radiating at a rate of a terawatt or more. And to get to this point, you’d have to wait more than half a duovigintillion (yes, there is such a number) years.

This question originally appeared on Quora. More questions on Quora:

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* Black Holes: What are some odd or generally unknown facts about outer space?

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