I've just read the following quote from the Wikipedia page on Hawking Radiation...

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).

From my understanding this is based on the law of Conservation of Energy.

E.g. an observer from outside the black hole will note a small area near the event horizon as initially having zero total energy, then within this area, virtual particles (or vacuum fluctuations) appear (which are allowed by the uncertainty principle), then the force of gravity pulls one virtual particle into the black hole while the other escapes. The observer now notes the particle escaping from the small area they are monitoring and that it has positive energy and concludes that the particle that fell into the black hole must have had negative energy (negative mass) to balance the positive.

From this it is concluded that the negative energy annihilates/cancels positive energy within the black hole and by this mechanism black holes can evaporate or loose mass.

I'm assuming that the particle and anti-particle (e.g. with positive and negative charge) are different from energy and negative energy and that it's just as likely that the anti-particle escapes the black hole as the particle (as both are effected by gravity equally).

So my questions are:

  1. Is my summary above correct?

  2. Is there any empirical evidence for negative energy (negative mass)?

There seems to be a very large (and IMO unproven) assumption that there was no energy coming into the small area being observed. So...

  1. Is it possible that the virtual particles are being created by something coming into the area from outside and colliding, e.g. neutrinos, dark matter, or some other charge-less particle?

  2. If we can't rule out external energy sources for the virtual particles then by Occam's razor shouldn't we take that as the simplest explanation and say that negative energy doesn't exist and black holes don't evaporate?

  • $\begingroup$ This question is related but there doesn't seem to be a consensus on whether the Hawking Radiation actually evaporates the BH or not (it depends on the frame of reference) and it doesn't address the question of whether the energy for the virtual particles could have an external source. $\endgroup$ – Quantumplate Dec 12 '14 at 7:39
  • $\begingroup$ I vote for $(4)$. I would argue the electrical charges from the physical particles in general would prevent the creation of a black hole. The AGN would instead eject a quasar relieving the pressure and recreating itself. $\endgroup$ – Cinaed Simson Aug 16 '19 at 8:36

It appears the main confusion here lies in the concept of a particle. So to simplify things, first consider flat space-time which is sufficient to discuss most of the issues here.

An accelerating observer in flat space-time will see an event horizon of a finite temperature, emitting particles. This is called Unruh radiation.

This is purely a coordinate system dependent effect. The particle "count" itself is coordinate system dependent. An inertial observer will not see this finite temperature horizon, and different accelerating observers will see different temperatures.

Someone free falling into a blackhole will not notice anything strange when passing the 'even horizon'. He will not see any particle / anti-particle pairs separating as you describe. An accelerating observer trying to maintain a small fixed distance above the blackhole's event horizon will see something analogous to that of an Unruh observer with the same proper acceleration.

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    $\begingroup$ Are you saying that observation of Hawking Radiation is dependent on your frame of reference and that depending on your frame of reference a black hole may appear to evaporate (and nothing is left) or it may not (and you still have a black hole)? $\endgroup$ – Quantumplate Dec 2 '14 at 9:24

The interaction between the BH and the particle antiparticle pair is so, that the negative energy particle will fall into the BH.

Now the particle antiparticle pair is in a superposition, they are indistinguishable.

It is very important to understand that the particle antiparticle pair is not the same as the negative and normal energy particle.

Particles and antiparticles both have normal energy. None of them have negative energy.

It is a vacuum fluctuation, and that creates a (virtual) particle antiparticle pair, but outside the event horizon. One of the particles falls into the BH, and the other not.

Because of conservation of energy, the one that falls in, needs to have negative energy. For a far away observer, the BH seems to have emitted a particle (and lost energy).

Since as per the SM, we have never experimentally seen a negative energy particle, when we observer the BH, the escaping particle cannot be the negative one.

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