Hawking Radiation: Does it Really Shrink Black Holes?

[Aeodyn]

I read about Hawking Radiation a while ago (Scientific American?), and just thought of something that seems to not agree with it:
Unless my memory is wrong, then at the event horizon the virtual particle pairs of the "vacuum" are split, and the anti-particle falls into the black hole, and the regular particle escapes. This antiparticle is then annihilated, shrinking it. And, when a particle and it's anti-particle annihilate, energy is released equal to their combined masses and energies. But that energy has the exact same gravitation as before annihilation, so the black hole should instead have gained mass, while still emitting hawking radiation, creating energy!

 

[bcrowell]

This antiparticle is then annihilated, shrinking it.

What do you mean by "shrinking?" These are pointlike particles.

And, when a particle and it's anti-particle annihilate, energy is released equal to their combined masses and energies. But that energy has the exact same gravitation as before annihilation, so the black hole should instead have gained mass, while still emitting hawking radiation, creating energy!

The particle and antiparticle don't annihilate. One escapes and one stays inside the event horizon.

 

[Aeodyn]

Sorry, I meant the black hole shrinking in gravitational pull.

Even if they don't annihilate. (That was just my understanding.)

 

[DaveC426913]

http://en.wikipedia.org/wiki/Hawking_radiation#Overview" describes the process simplistically:

...vacuum fluctuations cause a particle-antiparticle pair to appear close to the event horizon of a black hole. One of the pair falls into the black hole whilst the other escapes. In order to preserve total energy, the particle that fell into the black hole must have had a negative energy (with respect to an observer far away from the black hole). By this process, the black hole loses mass, and, to an outside observer, it would appear that the black hole has just emitted a particle.

 

[Aeodyn]

Oh... Did not see that bit!
Just wondering, why does it have - energy?

 

[DaveC426913]

Just wondering, why does it have - energy?

'it' what?

 

[Aeodyn]

The absorbed particle.

 

[yenchin]

This is a more detailed description: http://www.physics.ucdavis.edu/Text/Carlip.html#Hawkrad

 

[DaveC426913]

Oh... Did not see that bit!
Just wondering, why does it have - energy?

1] It came from net zero energy (vacuum),
2] The universe now contains a new particle that goes whizzing away from the BH, with its own energy (potential and kinetic),
3] Therefore, to maintain net zero (conservation of energy) the virtual particle must have had negative energy.

Negative energy doesn't have to be a real thing; it's just bookkeeping.

Look at it like this:

• The whole universe masses 100kg.
• Of that 100kg, 1kg is a black hole, (the other 99kg is everything but BH).

OK so far?

• Now, magically (i.e. through a process we don't know or care about), a 1g particle appears to be emitted out of the black hole into the universe at large.
• The universe still masses 100kg; now the part that is "not black hole" has a mass of 99.001kg.
• Therefore, the black hole now only masses 999g. It is evaporating.

 

[jnorman]

why can ONLY a negative energy particle fall into the BH? why can't the positive energy particle fall in?

 

[DaveC426913]

why can ONLY a negative energy particle fall into the BH? why can't the positive energy particle fall in?

The particle does not "have" negative energy; we interpret the end result as if it had negative energy. i.e. We "have" a real particle with real energy floating around, yet the net energy of the universe has not changed.


Vacuum energy means that particle-antiparticle pairs are always spontaneously popping into existence and then annihilating each other. Throughout, the net energy is zero. Even when the virtual particles are separate, the net energy is zero.

But if, halfway through the process, the two particles are unable to annihilate, because one falls into a BH, then the other one goes from being virtual to real. It now actually exists in our universe. By virtue of this fact, the kind of energy it must have is positive. The only real kind of energy in our universe is positive; we do not actually have negative energy.

By default then, the creation of positive energy in the form of this particle could just as easily be seen as if it were the destruction of negative energy. Note, this is not really negative energy, it is only bookkeeping. But it is a valid way of looking at the missing energy.


An analogy: Electricity: In an electrical wire, as 'negative electrons' move left, a 'negative potential' moves left. But it is often just as valid to view it as if there were 'electron holes' moving right, and thus a 'positive potential' moving right. (And in fact, engineers did and do exactly this. It is sometimes more useful.)

Sometimes things can be defined by what is not there.


Another (bad) analogy: You're driving in your car, trying to keep on-schedule and are calculating 60mph for one hour as your net speed. You'd say your trip was on-track (zero deviation from 60mph). If you slowed for construction, you would see your trip progress was in the negative. There isn't really a negative speed, it's just bookkeeping. It's brought about because you assume, mathematically, that 60mph=0.

 

[jnorman]

dave - thanks, but...why is it not okay for a negative energy particle to exist in our universe, but it is apparently okay for a negative energy particle to exist within the EH of a BH? there is no substantive difference between those two domains that i know of.

 

[LURCH]

Try thing about it this way:

Both virtual particles in the pair are made from energy that was inside the event horizon. When only one remains inside the horizon, and the other escapes, 1/2 energy that went into their creation has left.

Does that help?

 

[yenchin]

dave - thanks, but...why is it not okay for a negative energy particle to exist in our universe, but it is apparently okay for a negative energy particle to exist within the EH of a BH? there is no substantive difference between those two domains that i know of.

Did you read the link I posted? It's a long description, but somewhere there it says

"The criterion for it to continue to exist as a real particle is now that it must have positive energy relative to the timelike coordinate inside the horizon, i.e., that it must be moving radially inward."

As you crossed the event horizon, radial and temporal direction in the metric switches, so "negative" energy as defined by outside observer has positive energy relative to local observer that follows that particle into the black hole.

 

[Q-reeus]

From another forum site at http://forums.xkcd.com/viewtopic.php?f=18&t=61263 : "by doogly » Sun Jun 13, 2010 1:08 am UTC
Hawking Radiation has ABSOLUTELY NOTHING to do with particle-antiparticle spontaneous creation. This a heuristic picture someone came up that is actually more misleading than helpful. The derivation has nothing to do with them whatsoever. It has to do with complicated things like Bogolyubov transformations or operator algebras or whichever method you like, but they all involve lots of hard math. There is no easily accessible handwaving alternative. Sorry."
In other words, we non-specialists in 'quantum-field-theory-in-curved-spacetime' have been fed a load of hand-waving 'torus excreta', and arguing points based on eg. Calip's paper earlier cited (http://www.physics.ucdavis.edu/Text/Carlip.html#Hawkrad) only leads to more and more confusion. I mean, 'real' particle/anti-particle pairs only differ by the sign of charge & spin - energy is always real, equal and positive for both. So how does one of the virtual pair acquire -ve energy? To quote from Calip's paper: "To start, since we're talking about quantum field theory, let's understand what "energy" means in this context. The basic answer is that energy is determined by Planck's relation, E=hf, where f is frequency. Of course, a classical configuration of a field typically does not have a single frequency, but it can be Fourier decomposed into modes with fixed frequencies. In quantum field theory, modes with positive frequencies correspond to particles, and those with negative frequencies correspond to antiparticles." A physically meaningful 'negative frequency'? So now we have to chase after what that 'really' means. As noted earlier by Dave "Negative energy doesn't have to be a real thing; it's just bookkeeping."
There is a closely related topic often entitled 'Unruh effect', 'Fulling–Davies–Unruh effect' etc, and many regard Hawking radiation as a special case of the latter. Basically, it says an observer accelerating through the vacuum experiences a uniform bath of thermal radiation. The effect is normally incredibly small, see eg. http://en.wikipedia.org/wiki/Unruh_effect Originally I thought this must be either wrong or allows a perpetuum-mobile scenario. Why? Well, for instance inner-shell electrons in a heavy atom like lead have enormous average accelerations, and a back-of-the-envelope calculation suggests Unruh temperatures of the order of a few tens of thousands of degrees K - always a sizable fraction of the binding energy for that shell. OK so self-ionization won't happen but if 'real' you would expect the thermal jostling, integrated over all shell contributions, to be transferred to the atom as a whole. Not to speak of the much larger values for nucleon accelerations in the atomic core. Doesn't happen. If you read carefully the Wikipedia article cited above, there is a passage "In particular, there is no thermal radiation from the acceleration of the surface of the Earth, nor for a detector accelerating in a circle[citation needed], because under these circumstances there is no Rindler horizon in the field of view." So next chase up what a Rindler horizon is! Folks - my conclusion is; either spend years to become expert in the field, or just leave it all alone.

 

[Q-reeus]

Just came across an interesting article at http://arxiv.org/abs/0711.4767" Gives a quite accessible account of the meaning of negatve frequency wave packets and how it relates to Hawking radiation - replete with nicely colored illustrations and graphs. Note though there is a sentence "Hawking radiation may thus depend on as yet unknown physics or may not exist at all."