First let me identify myself as Benjamin Main, the original submitter. I want to thank imatfaal in particular for posting the original paper. I myself do not currently have the skills to make sense of much of the paper, not having had a proper training in the physics or accompanying mathematics that Hawking uses, though I hope to acquire some of the skills in my free time eventually.

That eventuality will not be soon enough for me to reply in a reasonable amount of time, so I'm going to have to rely on the illustrative language of Hawking's paper rather than the more precise mathematical elements. It seemed to me that the relevant illustrative language was here:

As the mass of the black hole decreased, the area of the event horizon would have to go down, thus violating the law that, classically, the area cannot decrease [7, 12]. This violation must, presumably, be caused by a flux of negative energy across the event horizon which balances the positive energy flux emitted to infinity. One might picture this negative energy flux in the following way. Just outside the event horizon there will be virtual pairs of particles, one with negative energy and one with positive energy. The negative particle is in a region which is classically forbidden but it can tunnel through the event horizon to the region inside the black hole where the Killing vector which represents time translations is spacelike. In this region the particle can exist as a real particle with a timelike momentum vector even though its energy relative to infinity as measured by the time translation Killing vector is negative. The other particle of the pair, having a positive energy, can escape to infinity where it constitutes a part of the thermal emission described above. The probability of the negative energy particle tunnelling through the horizon is governed by the surface gravity K since this quantity measures the gradient of the magnitude of the Killing vector or, in other words, how fast the Killing vector is becoming spacelike. Instead of thinking of negative energy particles tunnelling through the horizon in the positive sense of time one could regard them as positive energy particles crossing the horizon on pastdirected world-lines and then being scattered on to future-directed world-lines by the gravitational field. It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally. It should not be thought unreasonable that a black hole, which is an excited state of the gravitational field, should decay quantum mechanically and that, because of quantum fluctuation of the metric, energy should be able to tunnel out of the potential well of a black hole. This particle creation is directly analogous to that caused by a deep potential well in flat space-time [18]. The real justification of the thermal emission is the mathematical derivation given in Section (2) for the case of an uncharged non-rotating black hole. The effects of angular momentum and charge are considered in Section (3). In Section (4) it is shown that any renormalization of the energymomentum tensor with suitable properties must give a negative energy flow down the black hole and consequent decrease in the area of the event horizon.

This negative energy flow is non-observable locally.

This is a pretty long and fairly technical bit of writing in itself, but I think I can muster through in restating my concern in light of this part of the paper as well as restating the picture I had in my head as I wrote in the original email that is the opening post of this thread.

Part of the problem I had with the description by Andrew Pontzen and the similar one given by yor_on is the use of "anti-particle" in place of "negative energy particle" that is used by Hawking in the above vignette because "anti-particle" implies an antimatter particle (such as a positron), which is actually a

*positive* energy particle. So if you were to send in an antiparticle, you would still increase the energy of the black hole, which in the type of language used by Hawking above, would increase the area of the event horizon. Antimatter may have the opposite charge to its matter counterparts and they may mutually annihilate upon interaction, but the result is the release of energy in the form of gamma radiation. So, in the end, an antimatter particle would not affect a black hole any differently that

So the vignette I had in my head (and this may well have been derived from content of a previous Naked Astronomy podcast) was that you had a virtual particle-antiparticle pair arise near the event horizon and that while normally, such a pair would annihilate with no net energy change, if one of the pair crossed the event horizon and the other escaped the black hole's gravity well, there would be one real escaped particle and one real particle that was consumed by the black hole. The end result would again have to have no net change in energy, but since a particle escaped (and thus an amount of positive energy), there is energy lost by the black hole.

Now clearly, there are some differences between this vignette and the one described by Hawking, as rather than positing a particle-antiparticle pair, he posits a negative energy particle that tunnels across the event horizon with the positive energy particle escaping. Obviously, a negative energy particle would more concretely satisfy the condition of a negative energy flux across the event horizon than the scenario I described where there is an "energy debt" that arises from the creation of two positive energy virtual particles, one of which escapes.

Ultimately, as both Hawking and imatfaal point out, the actual mechanics of Hawking radiation are best described mathematically (and unfortunately in terms with which I am not yet familiar), so these vignettes are perhaps limited in their descriptive characteristics and maybe fixating on the details of what's ultimately an imprecise way of translating a more complicated and technical description into something intuitive to laymen such as myself is akin to asking how many angels can dance on the head of a pin.