Hawkings Theory

Ive posted this in another thread but it was old and didnt know if it would be read or not

I believe Hawkings theory to be wrong

Isnt the event horizion just a forbidden part of space that is only one way

It doesnt contribute to the mass of the black hole itself

So as a pair of virtual particles are created and one enters the black hole and one doesnt, it gains one particle but doesnt lose the other, as the other particle was just created in empty space

Applying it to our sun, if a pair of virtual particles are created in its gravitational field, one enters the sun and one flies into the emptiness of space, then it gains a particle but doesn't lose the other, as it never 'belonged' to it, it loses none of its mass, (It does by hydrogen burning but that isnt the context of this argument)

 

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Hawkings theory, I think, claims that black holes "evaporate" over time as high energy particles near the inside edge of the event horizon and "tunnel" across. Quantum tunneling is that part of the uncertainty principle where particles can exist anywhere but have a significant probability of existing in a certain place, which is where we say it is. But it could exist anywhere, or at least I think thats what they say. Dont take my word for it; look it up and make sure I am not totally off. And Hawkings theory doesnt quite sound that reasonable to me either...

 

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Hum,
A simple model of Hawkings radiation would be that virtual particles, (which are `entangled`) are created near the event horizon.
Now usually the virtual particles annihilate each other but now they cannot; the one sucked inside has to cancel out a bit of the black hole while the other particle has to cancel out something in the accretion disk/outside…
ie Electron and Positrons virtual particles for example would annihilate like this:
e + p -> gamma + gamma

But there are problems with this....

A more accurate model would be to use virtual photons, the photon is its own `anti particle` - thus we can the use negative mass energy to remove mass from the blackhole.

BTW,
Here is an another old thread about the `information` problem...

http://www.sciforums.com/archive/index.php/t-38685.html

It's an interesting read...

 

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i thought the virtual photon was just an exchange particle....

 

Hi all

Hawking's radiation is a semi-classical result. It follows from the fact that the black hole has a temperature and entropy. The thing about the particle pairs near the horizon is a handwaving explanation in layspeak that comes after the result, it's not the result itself.

 

So tell us what is the result.

Handwaving not permitted.

 

He'll need at least a whiteboard...

 

the event horizon is the point of no return for any object approaching a black hole.
so in effect it does add to a black holes mass.

 

Yeah,
its just a convenient mechanism to describe and produce the results.
The reality of whether a `virtual` photon really exists, or not, is perhaps a subject for another thread n the philosophy section.

 

Sure.

Briefly, Hawking extended a generalised quantum field into a specifically curved space-time: the schwarzschild geometry containing a collapsing black hole. The schwarzschild geometry is important for two reasons:
i) It's asymptotically flat, meaning you can recover particulate interpretations for your quantum field
ii) it's stationary and static

Hawking considered a linear quantum field propagating through the geometry from pre-collapse to long after collapse and calculated the particle content of the quantum field at infinity. He found a particle distribution corresponding to a blackbody emission spectrum. This result can be generalised to yield an emission spectrum from any arbitrary collapse into a late static state.

The blackbody spectrum yields a planck temperature for the black hole T = h-bar.c^3/8Pi.k.G.M), and since the temperature is non-zero the hole is the source of the radiation detected at infinity. Note that in this derivation there's no explicit consideration of the horizon surface - the particle counted is specifically conducted at infinity. Note also that the result is generalisable via the equivalence principle to accelerated observers in flat space-times containing a linear quantum field (quantum vacuum). Thus there's a flat space analogue for Hawking radiation called Unruh radiation.

 

Yes. This is another way to approach the problem (or, if you like, a driver for a solution). The Beckenstein-Hawking result that a hole has entropy proportional to its surface area (S=Akc^3/4Gh-bar) requires that the hole has non-zero temperature, and hence that it radiates.

 

I do not dispute this. In fact have posted observation that the energy that appears outside the event horizon can not be both particles (one of the vacuum polarization pair) and radition (Plank type with temperature your discuss) if one mechanism is responsible for the "evaporation" of small black holes.

I understand why the gravity gradient of a small black hole at the event horizon is greater than for a large black hole, so the idea that one of the vacuum pair got pulled in more frequently near small black hole makes some sense to me. (Small black holes should evaporate more rapidly.)

Is the surface temperature / entrophy of a small black hole also higher than for a large one? Surely the area of the event horizon is smaller for the small black hole than the big one. Thus for the "evaporation by radiation" idea to seem as reasonable as "evaporation by one of pair escaping" explanation, it is necessary that the surface be hoter the smaller the black hole is.

As In some sense, the entropy is related (I think) to the amount of information hidden in the black hole, this does not seem to be the case./

Can you set me straight? - I.e. support your claim that the pair production idea is "hand waving" compared to the Plank radiation idea. Personally I suspect both ideas are probably "hand waving" to the few who can actually treat this problem mathematically.

Let me close with a specific question: If the period in which energy of two electrons (approx 1Mev) need not be conserved were longer (giving more time for one of the vacuum pair to get pulled inside EH), are you stating there would be no change in the evaporation rate of small black hole?

 

You misunderstand me.

I didn't mention at all what the composition of the radiation was, only that it conformed to a planck spectrum at infinity. The actual radiation type is determined by the size of the hole - the wavelength of emitted radiation is on the order of the horizon size, and the emission frequency corresponds to the light crossing time of the horizon (this is a statistical QM result).

The next important thing to realise is that the gravitational field plays a role of "boosting" the radiation (ie the radiation steals energy from the field). There are no preferred modes of radiation, so any particle pair which can be produced will be produced.

Yes. The available energy in a field of strong curvature is higher, so it should provide more radiation. The handwaving explanation talks about this in terms of attenuation - the strong curvature increases the likelihood of pair separation. However from strictly classical considerations the hole's temperature is inversely proportional to its mass, so smaller holes must radiate more than larger holes.

The temperature is inversely proportional to the mass (and hence inversely proportional to the horizon area), however the entropy is directly proportional to the horizon area. So the larger the hole, the larger the entropy and the lower the temperature. As the hole radiates its temperature rises (hence increasing the radiaiton rate, and so on) but its entropy drops. This decrease in hole entropy is part of the information loss paradox.

Some physicists would agree with you - that information must be stored inside the hole (or holographically at the surface).

Without a rigorous understanding of quantum dynamics in strongly curved space-time, all we can do is wave hands and explore semi-classical results.

By "period in which energy of two electrons (approx 1Mev) need not be conserved", do you mean the hiesenberg uncertainty in time for energy del.E?

 

I no not understand much of anything in this area, so not too surprizing I missunderstood you. I do not even understand this "crossing time." My limitied knowledge in this area makes me think time goes very slow inside a black hole's EH. Is you "crossing time" the BH's EH diameter / c but that distance is far from the BH? or the distance actually inside the EH of the BH?...

Yes (I stated it this way as I do not know how to write the equation for Delta t limit, especially how to make "h bar" in a forum post. Glad you understood me.)

 

I tried to read Hawkings Universe years ago and got through most of it but I confess to having contracted a severe migraine for my efforts.

Hawking radiation is the result of sub-atomic particles spontaneously created near the schwarzchild radius appearing in pairs isn't it? One goes into the black hole never to return and the other becomes visible X rays? Yes or no? Thats my dumbed down understanding of it.

 

It's the time that a light signal would take to cross an idealised horizon surface. The bigger the BH the longer the crossing time, the lower the emission rate.

ok, so you're asking if a change in the value of the constant h-bar would change the emission rate? An increase in h-bar would mean an increase in the BH temperature, which would mean an increase in the emission rate (relative to now).

 

This is exactly what this thread is about. Did you read the thread?

 

Perfectly clear. Even if evaporation does occur, the resulting loss of mass is likely insignificant. A Black Hole could easily outpace the loss with intake of new matter. Complete evaporation is almost theoretically impossible.

Hawkings has a talent for pseudo-science. He was even forced to admit that Worm-Holes aren't possible. Now he's arguing that we should all pack up and go to Mars or the Moon. Why would I leave (even an admittedly failing atmosphere) for a place where the atmoshpere is toxic or where there is none at all? Earth has gravity that we are used to and a nice magnetic field to protect us from solar radiation. Earth would have to be reduced to rubble before it becomes more hostile than any where else.

My theory: Hawkings is a sci-fi nut with too much authority and not enough prudence.

 

Seconded

Bertrand Russell