ABSTRACT:
Hawking radiation has not been directly observed. Maybe it exists, maybe it doesn't. Even it it exists, some very fundamental physical laws prevent black hole evaporation. At the quantum level, Hawking radiation can be turned on its head. It could just as easily add mass to a black hole.
Hawking radiation has not been observed for a very good reason: it does not work the way you think. The hypothesis seems sound at first blush: Two particles pop into existence. One outside the black-hole horizon, and the other trapped inside the black hole. The outside particle escapes, and, can be deemed positive energy, since it adds energy to the outside universe. The trapped particle can be deemed negative energy since, according to Hawking, will reduce the black hole's mass. Note that energy is always conserved, since positive energy and negative energy mathematically cancel each other. The bottom line is black holes allegedly evaporate due to Hawking radiation. I say "allegedly" because there is more to the story. The Hawking-radiation hypothesis is incomplete. Let's do a more complete thought experiment and see what happens.
Imagine a star that is virtually all matter, with next to no anti-matter. The star collapes into a black hole. Its mass is still composed of virtually all matter. The stuff that falls into this black hole is virtually all matter. In the black-hole diagram below, we represent a particle of this matter with the Greek letter mu preceded by a plus sign. Ellipses before and after the plus mu's represent multiple particles that may have been crushed into a singularity.
The above diagram represents the starting mass and the state prior to the appearance of a particle (plus mu) and an antiparticle (minus mu). The next state below is where a particle-antiparticle pair appears. The antiparticle escapes the black hole's gravity, but the particle is trapped.
In the next diagram the trapped particle has no anti-particle to interact with, so it adds mass to the black hole! This particle can be deemed the positive energy. The escaped anti-particle is then deemed negative energy and has the potential to interact with any particle it encounters. Such interaction will reduce the mass of the universe outside the black hole.
Of course there is only a 50% probability the black hole will gain mass and the remaining universe will lose mass. Below we see that there is a 50% probability that the particle will escape and the antiparticle is trapped.
The antiparticle has no problem finding particles to interact with:
The black hole loses the mass it previously gained:
The escaped particle and the escaped anti-particle may annihilate each other, or, if they are too far apart, will interact with other particles and antiparticles.
The space outside the black hole returns to nothing and the black hole returns to its starting mass:
The above thought experiment can also be performed with anti-matter black holes. The main problem with Hawking's hypothesis is it has the following implicit assumption: That all black holes have fairly equal amounts of matter and anti-matter. One might ponder whether a star that precedes a black hole can have fairly equal amounts of matter and anti-matter and still exist. Assuming the answer is a resounding no, then black holes don't evaporate via Hawking radiation.
For the sake of argument, let's assume Hawking was right. There is Hawking radiation and it causes black holes to evaporate. Why should black holes have all the fun? Imagine a particle-antiparticle pair appearing above the earth's surface. One escapes earth's gravity, the other does not. When they first appeared, they each had velocity v which is less than light speed. Velocity v was an escape velocity for one but not the other--the other being too close to earth's center of mass. If Hawking was right, the trapped particle should reduce the earth's mass. Over time the earth will completely evaporate. Thus, if Hawking was correct, all planets, stars, etc. should evaporate. The counter-argument is no such evaporation has been observed.
The equations below further demonstrate why black holes, in particular, refuse to evaporate:
Since light can't escape a black hole, a black hole's emissivity is zero. Even if it has an emissivity of one, power (P) according to the Stefan-Boltzmann equation above, is less than zero. This implies there is more radiation entering a black hole than randiation escaping. The minimum mass required to make a black hole is approximately three solar masses. So much mass causes the black hole's temperature to be less than its surrounding environment: deep space. The second law of thermodynamics would be violated if the net thermal transfer favors black-hole evaporation. Black hole entropy increases when a black hole's mass increases:
On the flip side, a compelling argument in favor of black-hole evaporation is the following thought experiment: Imagine a photon-antiphoton pair. Photons and antiphotons are indistinguishable from each other. So if the photon is trapped, it could behave like an antiphoton and annihilate matter inside the black hole, reducing the black-hole's mass. However, the escaped anti-photon can also behave like an antiphoton. If the escaped antiphoton finds another photon first, it becomes the negative-energy particle and reduces the energy of the universe outside the black hole. The trapped photon (or antiphoton) will add energy or mass to the black hole.
Photon-antiphoton Hawking radiation is more likely to cause the black-hole to lose mass if the black-hole's surrounding environment is empty space with a lower temperature. Albeit, this is an ideal and unrealistic condition. The cosmic microwave background raises the temperature of the surrounding environment to approximately 2.73 Kelvin, well above the temperature of the typical black hole. Thus, the following scenario is consistent with equations 1 through 6 above: The escaped photon is more likely to find another photon to interact with. When it does, the two photons vanish. The trapped photon adds mass to the black hole.
References:
1. Hossenfelder, Sabine (23 August 2019). "How do black holes destroy information and why is that a problem?". Back ReAction. Retrieved 23 November 2019.
2. Hawking, Stephen (1 August 1975). "Particle Creation by Black Holes" (PDF). Commun. Math. Phys. 43 (3): 199–220.
3. Susskind, Leonard (2008-07-07). The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics. Little, Brown and Company.
4. Black hole information paradox. Wikipedia.
5. Mathur, Samir D. 03/21/2021. The Elastic Vacuum. Gravity Research Foundation.
6. Chaisson, Eric. Astronomy Today. Englewood, NJ: Prentice Hall, 1993: 503
7. Severino, Paul. THe Black Hole Information Paradox: A Quantum Information Perspective. 03/24/2020
8. Wilkins, Alex. Ilands Poking Out of Black Holes May Solve the Information Paradox. 01/11/2024. UC Berkeley Physics.
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