In this blog we have presented reasons why the various derivations of Hawking or Unruh radiation are flawed. The main obstacle in the proofs is that they break conservation of energy or momentum. At this point it looks like Hawking or Unruh radiation does not exist. All the derivations use flawed quantum field theory.
We are not alone in our skepticism. Vladimir Belinski, Detlev Buchholz, and some other researchers have come to similar conclusions in the past 25 years.
Let us look at an analogous black hole, a sonic or acoustic black hole, where the "horizon" forms at the point where the speed of a liquid flow, measured in the laboratory frame, exceeds the speed of sound in the liquid.
https://www.nature.com/news/artificial-black-hole-creates-its-own-version-of-hawking-radiation-1.20430
"On one side of his acoustical event horizon, where the atoms move at supersonic speeds, phonons became trapped. And when Steinhauer took pictures of the BEC, he found correlations between the densities of atoms that were an equal distance from the event horizon but on opposite sides. This demonstrates that pairs of phonons were entangled — a sign that they originated spontaneously from the same quantum fluctuation, he says, and that the BEC was producing Hawking radiation."
Jeff Steinhauer from Technion, Haifa, claims to have observed Hawking radiation in the form of phonons.
The classical limit of sonic Hawking radiation
A basic result, or in some cases an assumption, in derivations of Hawking radiation is that a freely falling observer close to the horizon sees a vacuum, that is, no vibrations or sound.
An often cited derivation claims that a static observer close to the horizon must see the space as "warm", that is, energy quanta in space, if the freely falling observer sees a perfect vacuum.
Suppose that we have several microphones close to the horizon of a sonic black hole, and they register very many coherent phonons of Hawking radiation in a short time interval. Since the radiation is random, there is a non-zero probability of seeing such an event.
But many coherent phonons mean that there is a classical sound wave. A freely falling observer must see such a sound wave. The freely falling observer can measure the density of the liquid around him and detect it is varying around him. This is a contradiction, because we assumed that the freely falling observer sees a perfect vacuum.
In the quote above, Jeff Steinhauer says that he has "taken pictures" of density fluctuations around the horizon. Taking pictures suggests that the density fluctuations are a classical sound wave. That contradicts the basic assumption that the freely falling observer sees a perfect vacuum.
How would sound waves know where the horizon is?
How would atoms in the liquid know that they are at the horizon, so that they know to produce phonons?
The location of the horizon is defined as the point where sound waves stand still relative to the laboratory frame. If the fluid flows undisturbed, how do the atoms know what is the rest frame of the laboratory?
If the fluid is in a vessel whose walls are at rest relative to the laboratory, then the atoms might detect the laboratory rest frame by receiving some signal from the walls. But this is in contradiction with the assumption that the freely falling observer sees a perfect vacuum.
Entropy
If microphones receive phonons, where does the energy of these phonons come from? Obviously, the liquid must lose some of its kinetic energy to produce the phonons. The kinetic energy of the liquid is translational, it has an extremely low entropy. Produced phonons have a much higher entropy.
What process is able to increase the entropy in the experiment? Usually, it is friction which produces high-entropy energy, but we were assuming that the liquid is perfect and flows without any kind of disturbance.
Momentum conservation
If the liquid loses some of its kinetic energy, where does the extra momentum go? It apparently has to be absorbed by the walls of the vessel, if the liquid is in a vessel. But if the acceleration of the liquid is done without any vessel walls, what in that case absorbs the surplus momentum?
Conclusions
It looks like no analogous Hawking radiation, in the form of phonons, can exist in a sonic black hole.
We still need to look at the papers by Unruh and Steinhauer, if they have addressed the contradictions we uncovered above.
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