1. I've recently been reading a very interesting book called "The Trouble with Physics" by Lee Smolin (a quantum gravity theorist) and came across a part explaining black holes and how physicists such as Jacob Bekenstein and Stephen Hawking discovered various features of black holes. So, as the book says, it was found that the temperature of black hole is inversely proportional to the mass of the black hole- so by adding mass to the black hole (as it draws matter in) it cools down. It also goes on to say that "Hawking realised that (as with any body with a temperature), a black hole must emit radiation. This radiation carries energy away from the black hole. Given enough time, all the mass in the black hole will turn into radiation... the black hole gets lighter... and, when it loses mass it heats up and so radiates faster and faster".

So, my question is- why does the black hole get hotter and lose mass over time? Why doesn't the amount of mass entering the black hole cool it down and counteract the radiation emission? Or is it 'simply' a case of the rate of radiation from the black hole is faster than the rate of mass accumulation and so the net effect is temperature gain and mass loss? But I don't see how this could work- surely the black hole can only convert the mass it gains into radiation and no more: so how could the rate of black hole radiation be higher than mass gain and cooling down?

2.

3. Hawking's statement assumes nothing is coming in.

4. How does this work?

5. What is being talked about is Hawking radiation. It is a quantum mechanical effect that can occur at the event horizon.

Virtual particles are constantly popping in and out of existence. They are created in matter-antimatter pairs from "borrowed" energy. As long as the loan is paid back in a timely manner (as determined by the uncertainty principle) everything is fine. The energy is paid back by the two particles rejoining and annihilating each other.

From time to time one of these virtual particle pairs forms near the event horizon and before they rejoin, one of the pair fall inside the event horizon while the other doesn't. When this happens, they cannot rejoin. The particle outside the event horizon becomes real. The energy of the particles must still balance so the particle inside the event horizon takes on a negative energy. This negative energy cancels out some of the mass of the black hole, which "pays back" the loan.

Hawking radiation causes the Black hole to leak away its mass. The smaller the black hole, the more pronounced the leakage and the faster the black hole bleeds away.

Now, even the most lonely black hole is still taking in energy in the form of the Cosmic back ground radiation. So as long as a BH is massive enough to be cooler than ~4°K, it will take in energy faster than it bleeds it away. You would need a BH less massive than the Earth for this to occur.

6. Ah, ok. That makes sense, I've read a bit about 'virtual particles' and the uncertainty principle before- I never realised that the two topics of Hawking radiation and uncertainty principle were so intrinsically linked! That's what I love about physics, it can all be unified (well, nearly all- the grand theory of unification of all fundamental forces etc is still being worked on)...

7. Originally Posted by x(x-y)
I've recently been reading a very interesting book called "The Trouble with Physics" by Lee Smolin (a quantum gravity theorist) and came across a part explaining black holes and how physicists such as Jacob Bekenstein and Stephen Hawking discovered various features of black holes. So, as the book says, it was found that the temperature of black hole is inversely proportional to the mass of the black hole- so by adding mass to the black hole (as it draws matter in) it cools down. It also goes on to say that "Hawking realised that (as with any body with a temperature), a black hole must emit radiation. This radiation carries energy away from the black hole. Given enough time, all the mass in the black hole will turn into radiation... the black hole gets lighter... and, when it loses mass it heats up and so radiates faster and faster".

So, my question is- why does the black hole get hotter and lose mass over time? Why doesn't the amount of mass entering the black hole cool it down and counteract the radiation emission? Or is it 'simply' a case of the rate of radiation from the black hole is faster than the rate of mass accumulation and so the net effect is temperature gain and mass loss? But I don't see how this could work- surely the black hole can only convert the mass it gains into radiation and no more: so how could the rate of black hole radiation be higher than mass gain and cooling down?

8. That's all very well, Dr. Rocket, but it's a little (well, quite a lot) too advanced for me at this time- I'm only doing A-Level Physics and Mathematics (and Chemistry and Geography) at the moment!

9. Originally Posted by x(x-y)
I've recently been reading a very interesting book called "The Trouble with Physics" by Lee Smolin (a quantum gravity theorist) and came across a part explaining black holes and how physicists such as Jacob Bekenstein and Stephen Hawking discovered various features of black holes. So, as the book says, it was found that the temperature of black hole is inversely proportional to the mass of the black hole- so by adding mass to the black hole (as it draws matter in) it cools down. It also goes on to say that "Hawking realised that (as with any body with a temperature), a black hole must emit radiation. This radiation carries energy away from the black hole. Given enough time, all the mass in the black hole will turn into radiation... the black hole gets lighter... and, when it loses mass it heats up and so radiates faster and faster".

So, my question is- why does the black hole get hotter and lose mass over time? Why doesn't the amount of mass entering the black hole cool it down and counteract the radiation emission? Or is it 'simply' a case of the rate of radiation from the black hole is faster than the rate of mass accumulation and so the net effect is temperature gain and mass loss? But I don't see how this could work- surely the black hole can only convert the mass it gains into radiation and no more: so how could the rate of black hole radiation be higher than mass gain and cooling down?