[Confuses]

In a brief history of time it says theft 'according to the uncertainty principle rotating black holes should emit particles'. However I do not understand why rotating black holes need to emit particles according to the uncertainty principle.

I do understand why black holes emit particles it is just the rotating black holes and The uncertainty principle thing that I do not understand.

Thanks in advance.

[Joinedup]

Afaik you're talking about p104 of the hardback.
It appears hawking is saying the older idea about rotating black holes is wrong and his idea about any black hole is right, or at least widely accepted.

[3nTr0pY]

(Original post by Confuses)
In a brief history of time it says theft 'according to the uncertainty principle rotating black holes should emit particles'. However I do not understand why rotating black holes need to emit particles according to the uncertainty principle.

I do understand why black holes emit particles it is just the rotating black holes and The uncertainty principle thing that I do not understand.

Thanks in advance.

Really interesting question but the answer is difficult to follow if you haven't studied much physics. I'll try and explain it nevertheless although I shall do so for non-rotating black holes which give qualitatively the same effect. Here's how:

Heisenberg's Uncertainty Principle in quantum mechanics can be applied to energy and time. What it says is that if the time over which measurements are made is very short (giving low time uncertainty), the uncertainty in the energy will be very large. So on short time scales, conservation of energy (energy-momentum to be precise) does not apply exactly and so 'virtual' particles and anti-particles (which have positive energy) are often created and destroyed. Annihilation occurs when the particle collides with the antiparticle.


Now imagine this process, known as 'pair creation', occurring just outside the event horizon of a black hole, the event horizon essentially being the point of no return, where not even light can escape the gravitational pull. Now a really strange thing happens in a black hole as a consequence of the application of Einstein's equations: once the event horizon is passed, space becomes time and time becomes space. Unfortunately you probably need a working knowledge of General Relativity to know why this is true. Please just take it as a given and consider this:

Pair creation requires the overall energy to be zero after short periods of time and so particle-antiparticle annihilation must occur very rapidly. This is because both particles and antiparticles have positive energy and so annihilation is the only way of going back to zero energy. However, if just one particle crosses the event horizon of a black hole it feels time and space switch round and this essentially makes its energy become momentum. Since the particle and antiparticle are separated annihilation is impossible, but the overall energy-momentum must still be zero. This is only possible if the particle inside the event horizon has negative momentum. The switching of time and space coordinates allows energy to be manifest as negative momentum ensuring the overall energy-momentum is conserved.

Thus positive energy particles are seen to be emitted by the black hole and over time the black hole decreases in mass or 'evaporates'. This is known as Hawking radiation. One should note that although it is widely predicted by those in the know to be a real effect, Hawking radiation during the life of a black hole is too tiny to detect. Hawking radiation predicts a massive burst of energy at the end of a black holes life. Unfortunately no such events have ever been seen.

[ben-smith]

(Original post by 3nTr0pY)
So on short time scales, conservation of energy (energy-momentum to be precise) does not apply exactly

Can you expand on this? I thought momentum/energy was always a conserved current which you can show using Noether's theorem (explicitly, using the homogeneity of space and time).

[3nTr0pY]

(Original post by ben-smith)
Can you expand on this? I thought momentum/energy was always a conserved current which you can show using Noether's theorem (explicitly, using the homogeneity of space and time).

I was actually being a little misleading in that comment as I didn't want to confuse the issue with too much formalism. Actually it is the expectation of the energy-momentum that is conserved in quantum mechanics, so I presumed that the energy itself can vary on short time scales (certainly virtual particles make it appear to do so) but I have no rigorous understanding of what's going on.

There's a discussion of this issue here:

http://www.physicsforums.com/showthread.php?t=120224

To be honest, I'm not really sure on the issue and have not thought it through in detail/ nor read the link in detail, but I may have a think about it over the next few days.