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I'm doing some research on black holes for a science video contest - more specifically, on Hawking Radiation. As far as I know, there are these constant quantum fluctuations of "virtual" particle pairs (basically particle-antiparticle) that appear, then almost instantaneously mutually annihilate. Near the event horizon of a BH, if one virtual particle gets trapped inside, then it acquires negative energy, while the other particle escapes away and is emitted as radiation. My question is, why does the virtual particle that's sucked in get negative energy? Is it due to some rotating vector stuff or is it inherent in the particle? And, as per my logic, if NASA detected this image of a BH, it's clear that it's emanating some radiation, so Hawking Radiation has to exist, right?

Any help in clarifying or correcting my understanding would be appreciated.Thank you.

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Unless everything we know about general relativity and quantum field theory is wrong, Hawking radiation almost certainly exists.

It is also entirely undetectable. The thermal output of a 3 solar mass black hole by way of Hawking radiation amounts to $\sim 10^{-29}$ W. This, of course, is not only completely undetectable but the corresponding Hawking temperature, $\sim 2\times 10^{-8}$ K, is far, far below the temperature of the CMB; so any astrophysical black hole today would absorb many orders of magnitude more radiation from the CMB than it emits by way of Hawking radiation.

The explanation with virtual particle-antiparticle pairs and negative energy particles absorbed by the black hole originates, I believe, from Hawking's popular science book A Brief History of Time, but it really is at odds with Hawking's own groundbreaking paper on the subject (Nature 248, 1974). This is explained quite nicely in an informative article by Ethan Siegel, published last year online: https://www.forbes.com/sites/startswithabang/2020/07/09/yes-stephen-hawking-lied-to-us-all-about-how-black-holes-decay/?sh=52d60ad44e63 .

Adding to Ethan's explanation (which is well worth the read) I ought to mention two things. First, there is the closely related concept Unruh radiation: thermal radiation seen by an accelerating observer from the direction of his apparent Rindler-horizon, in spacetime that is seen as empty by an inertial observer. This alone stresses the important point that in quantum field theory, the concept of a particle becomes observer-dependent once we permit accelerating observers and/or gravitational fields. Second, the wavelength of Hawking radiation alone should tell us that it is not originating from the event horizon. For the aforementioned three solar mass black hole, the peak wavelength is almost 180 km. Comparing this to the less than 10 km Schwarzschild radius of the black hole, I think it is quite evident that this is not about particle-antiparticle pairs at the horizon itself.

Finally, regarding the images of the M87* supermassive black hole, first, these are not NASA images but images produced by an international collaboration called the Event Horizon Telescope project. Second, though they are often described as images of the black hole, that is not strictly correct. What you actually see is radio frequency emissions of infalling matter surrounding the black hole in the form of an accretion disk. The central, black shadow corresponds to the black hole's photon sphere (radius at which unstable closed photon orbits become possible). And it is important to remember that this is not exactly a photograph, but rather, a synthesized image that is fitted to a large number of radio frequency observations using an optimization method.

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