From my Stargate book (still not finished)
1974: Hawking shows that all black-holes radiate black body radiation[i] whose peak wavelength l_{max} is roughly the square root of the area-entropy of the black-hole’s horizon, i.e., l_{max} ~ A1/2 where the entropy S ~ k_{B}A/4.
Kip Thorne’s book “Black Holes and Time Warps” (1994) gives the best popular explanation of Hawking’s horizon evaporation radiation and the history of its discovery including the role of Zeldovitch in the Soviet Union some forty years ago. Zeldovitch arguing by analogy to the electrodynamics of a rotating neutral conducting sphere said that the virtual photons of the zero point vacuum fluctuations would “tickle” the metal like spontaneous emission of light triggered by virtual photons interacting with real electrons in excited atoms, the rotational energy of the sphere then converting to real photons. Hawking was with Zeldovitch at Les Houches in France. Some time later Hawking, using Bekenstein’s thermodynamics of horizons where the temperature is proportional to the inverse square root of the horizon’s area-entropy A. That is T_{cold} ~ A^{-1/2}. I realized in 2013 that this is only half the story, and that there is a second higher temperature T_{hot} ~ (LA^{1/2})^{-1/2}, which is the proper quantum thickness of the horizon. For example, when L = Planck length we have gravity wave Hawking horizon thickness radiation, when L = Compton wavelength we have electromagnetic radiation from properly accelerating real electrons and positrons. There will also be a sharp gamma ray signal from electron-positron annihilations outside the black-hole horizon. Indeed, the horizon, in the stretched membrane description, is a heat engine of high maximal efficiency ~ 1 – (L/A^{1/2})^{1/2}. Returning to Kip Thorne’s narrative, Zeldovich was convinced the mostly gravity wave rotation radiation would stop when the black-hole stopped rotating from Kerr metric to Schwarzschild metric. However, Hawking did rough calculations suggesting that even stationary black-holes would evaporate mostly by gravity wave emission, although all kinds of thermal emission of every type would also occur. Kip Thorne wrote:
There are several different ways to picture black-hole evaporation … However, all the ways acknowledge vacuum fluctuations as the ultimate source of the outflowing radiation … The waves fluctuate randomly and unpredictably, with positive energy momentarily here, negative energy momentarily there, and zero energy on average. The particle aspect is embodied in the concept of virtual particles, that is particles that flash into existence in pairs (two particles at a time) …
And they are quantum entangled as in the EPR effect.[ii]
… living momentarily on fluctuational energy borrowed from neighboring regions of space, and that then annihilate and disappear, giving their energy back to the neighboring regions. For electromagnetic vacuum fluctuations, the virtual particles are virtual photons; for gravitational vacuum fluctuations, they are virtual gravitons. … a virtual electron and a virtual positron are likely to flash into existence as an [entangled] pair … the photon is its own antiparticle, so virtual photons flash in and out of existence in [entangled] pairs, and similarly for gravitons. …
The way the phenomenon appears depends on the local frame of the observer. First for the LIF non-rotating timelike geodesic observer in weightless free float:
A black-hole’s tidal gravity pulls an [entangled] pair of virtual photons apart, thereby feeding energy into them … The virtual photons can separate from each other easily, so long as they both remain in a region where the electromagnetic field has momentarily acquired positive energy … the region’s size will always be about the same as the wavelength of the fluctuating electromagnetic field … If the wavelength happens to be about the same as the hole’s circumference [~ A1/2], then the virtual photons can easily separate from eac