According to the chapter on evaporation in the "Black Hole" entry on Wiki: https://archive.md/ocwUV :"This emission of particles occurs stochastically on the horizon of a black hole, so macroscopically it appears as if the black hole is glowing with thermal radiation at a certain temperature. This is called Hawking radiation (or Hawking emission). By losing energy through this radiation (energy is equivalent to mass), the mass of the black hole decreases. The temperature T of Hawking radiation is inversely proportional to the mass M of the black hole, and can be expressed by the following formula:
T = hc^3 / (8π^2 * GMk)
(Here, π is pi, G is the gravitational constant, and k is the Boltzmann constant.)
In a small black hole with a mass similar to that of a proton, this quantum effect cannot be ignored. When mass decreases due to Hawking radiation, this effect becomes stronger, increasing the intensity of the radiation, accelerating the loss of mass and energy, and eventually causing the black hole to explode and disappear.
In a black hole just before it disappears, the temperature can reach 10^32 K.
This is the evaporation of a black hole." (Note 1)
Basically, according to the paradigm of "BH evaporates and disappears," there are articles like the following:
"Problems with Quantum BH": https://archive.md/XVDlU ：According to this article, virtual particles and virtual antiparticles are created and then disappear in the vacuum near the horizon.
Among them, there are virtual particles that jump into the BH beyond the horizon.
According to Hawking's calculations, these virtual particles are said to bring "negative energy into the BH."
The remaining virtual particle that was not absorbed by the BH becomes a real particle and flies away from the BH.
Therefore, the BH loses energy by the amount of the virtual particle that jumped in, and its mass becomes lighter by that amount.
On the other hand, the real particle that emerged from the virtual particle that jumped into the BH carries positive energy to offset the negative energy, and it appears to escape (from the observer outside the BH).
This is roughly the mechanism of Hawking radiation, where the BH appears to have a temperature and emit thermal radiation to an observer outside the BH.
By continuing this Hawking radiation, the mass of the BH gradually decreases and eventually the BH evaporates and disappears from this world, as Hawking said.
Well, there are some who have expressed the opinion that Stephen Hawking's calculations may be a bit off, but the general consensus is that 'black holes do emit Hawking radiation' and that 'as a result, black hole mass decreases' (Note 1).
Furthermore, it is widely believed among physicists that the black hole will disappear when the Hawking radiation reaches its final stage. However, there are a few physicists who hold the minority opinion that the fate of a black hole that has shrunk to the Planck level is unknown and that it may maintain its black hole state stably thereafter.
As for myself, I argue that 'a black hole that has shrunk to the Planck level will stop emitting Hawking radiation at that point and will continue to maintain its black hole state stably.'
Why do I make this claim? It's because the process of Hawking radiation starts with 'virtual particles first entering the black hole.' In contrast, in the case of normal thermal radiation, there is no need for anything to enter the object emitting radiation, as long as the object emits heat. However, in both cases, whether the object is ordinary matter or a black hole, 'radiated energy causes the object's mass to decrease.'
In the case of a black hole, however, one of the virtual particles that was born in pairs near the black hole must first enter the black hole. Therefore, in a black hole that has become so small that its horizon diameter is below the Planck scale, there can be no virtual particles that can enter it. This is because, as string theory proposes, 'all elementary particles have a finite size.' It is said that the smallest size that a particle can have is about the Planck scale.
If this is the case, then a black hole that has shrunk to a diameter below the Planck scale due to Hawking radiation will not allow anything, including elementary particles, to enter it. Therefore, it cannot emit Hawking radiation.
From the above considerations, it can be argued that the massive number of primordial black holes born at the very beginning of the universe, which were about the Planck scale in size, still exist as dark matter filling the universe today.
However, many physicists are trapped in the 'Hawking Trap,' holding onto Hawking's statement that 'black holes emit Hawking radiation and eventually disappear.'
Note 1: For details on the derivation of the lifetime equation, please refer to "Hawking Radiation and Black Hole Evaporation": http://astro-wakate.sakura.ne.jp/ss2013/web/syuroku/grcosmo_24a.pdf：.
However, there may be typographical errors in some of the formulas used in the derivation, but the concluding formula appears to be correct.
For more detailed results on modern lifetime equations, please refer to "Hawking Radiation": https://en-m-wikipedia-org.translate.goog/wiki/Hawking_radiation?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja&_x_tr_pto=sc：.
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