View Full Version : Question about Hawkings Radiation

2009-Mar-20, 10:41 PM
What is the distance away from the EH that a Virtual Partical needs to be in order to be spilt by the gravitational force of the BH?

What is the relative time dilation at that point?

2009-Mar-21, 09:34 PM
anyone? My thought here is that there is an exact point away from a black hole that hawking radiation can happen. Otherwise it would either be too far away and the VP would not be split OR both would get gobbled up by the BH.

2009-Mar-21, 10:50 PM
Well, for the time dilation, there's a nice bit on the wiki.


But as for the virtual photon splitting distance...that's beyond me.

2009-Mar-22, 01:00 AM
anyone? My thought here is that there is an exact point away from a black hole that hawking radiation can happen.

Black holes might not have any hair, but they're all different. :) So it depends on the hole characteristics. Don't forget you might also be considering some very intense frame dragging, complicating the calculation. And of course virtual particles come in a variety of energies, which may also affect the range of possibility within which Hawking radiation might occur....

2009-Mar-22, 12:09 PM
As no one else seems to know, I'll have a go.

Hawking Radiation is due to the separation of virtual particles at the Event Horizon that would otherwise self-annihalate. This is also seen in the Casimir Effect (QV) in which two parallel plates are separated by a very small distance. By disturbing the quantum soup of virtual particles between them, a 'vacuum pressure' appears between the plates, and they are drawn together. The smaller the separation, the higher the pressure but it is 100kPascals when the separation is 10 nanoMeters.
So by analogy (never a good argument), Hawking radiation will appear to arise that close to the Event Horizon.

Time dilation? As an object approaches the EH, time slows until at the EH it becomes infinitely slow to an outside observer. Light from such an object is red shifted, and HR is also red shifted. Now I pass beyond my own horizon, as while it should be possible to calculate the spectrum of radiation from HR at the horizon, and to use the observed red shift to calculate the time dilation where it originates, I can't do that.

Over to the gurus!


2009-Mar-22, 04:07 PM
I'm not going to answer the questions because they're not real questions.

I suggest thinking about the EH as if it were a rainbow or an equator. They're not real objects, but we all agree they exist. Just like the rainbow, everyone sees their own EH depending on their location and motion. Again like a rainbow, the EH is an optical effect that cannot be touched. As you move towards it, the image just keeps shifting.

Classical thinking needs to recognized for what it is, classical thinking. It's always an approximation and gives little to no information about the processes involved.

An event horizon is not a classical thing. Time dilation has to do with General Relativity and moving between reference frames. It is meaningless to say the time dilation at the EH since you haven't specified a finish line. The dilation as compared to someone on Earth, someone just beyond the photon sphere?

If we both let ourselves fall into a BH(without drifting apart) and compare our watches, there will be no slowing. Our watches will only stop once they physically break apart. Until then we will happily be exchanging notes; at and beyond the EH of a supermassive BH.

2009-Mar-22, 05:01 PM
The smaller the separation, the higher the pressure but it is 100kPascals when the separation is 10 nanoMeters.

Tommac/John. 1.Since atmospheric pressure on a normal day at sea level is ~ 100 kPascals...I think somebody reporting that as Casimir is seeing the two plates touch each other, in which case...the weight of the atmosphere on the top plate, plus the weight of the top plate....is now on the bottom plate, like a football game pigpile.
2. There is no reason to assume that matter will fall into the EH, and antimatter out ...(or you would have to suppose that GR treats their masses differently, and it doesn't, as far as I know). So, in a random sort sort-of-way, equal amounts of matter and antimatter escape the EH, and annihilate anyway. The Eh doesn't act like some magical cosmic sieve, giving us more matter at the expense of the mass/energy of the BH. :cool:

2009-Mar-23, 12:13 PM
Bad idea to quote it in kP - pressure is force/unit area, and I had no idea what that area might be. But the whole point of the Casimir Effct is that it is detected IN A VACUUM (vacuum pressure??) which you really should have known before you started writing about atmosperic pressure.

This is from a Physics World article: http://physicsworld.com/cws/article/print/9747

"For example, two mirrors with an area of 1 cm2 separated by a distance of 1 Ám have an attractive Casimir force of about 10-7 N - roughly the weight of a water droplet that is half a millimetre in diameter"

That's 10^-3N/m^2 or 0.01kP, so that previous figure must have come from an experiment that involved plates 10,000 times bigger!

Hawking himself is aware of the problem you have with why the escaped virtual particles are real, not a mixture of matter and antimatter, that would cancel out. His explanation is (I think) that a virtual antimatter particle that is captured REDUCES the mass of the BH, so it is as if a real particle escapes.
Causality makes it so as two real particles escape when one antimatter is captured. The alternative of a real being captured and the antimatter escaping leads to no escaped particles, but energy release and a net loss from the BH.

Causality makes me worry, so you could argue that an escaped real particle is a net loss to the BH (the antimatter reduces the BH mass), while the escaped antimatter releases energy equivalent to the capture4d real particle into the universe outside the BH. So either way, the BH has hair!