Correction to black hole radiation due to pair annihilation

Abstract

We consider the emission of charged scalar particles from a Schwarzschild black hole. It is shown that these particles can interact with each other through pair annihilation, and as a result, produce photons. These photons make a correction to the spectrum of photons that are directly emitted from the black hole. By solving field equations using the WKB approximation, the pair annihilation rate is taken into account for the most probable case, i.e., the first order, and therefore the correction will be of the order of e2. Considering this scenario, we show that most interactions take place near the event horizon of the black hole, yet the number of interactions is not large enough to make a remarkable modification in the radiation spectrum of particles.

Quantum vacuum effects on the formation of black holes

“…The temperature of the Hawking radiation of a black hole has an inverse relationship with its mass, in other words, the smaller the black hole's mass, the higher its Hawking radiation will be. Therefore, for small black holes [62], evaporation is to the extent that their gravitational mass should be considered as a function of time, while it takes 10 67 years to completely evaporate a black hole with the mass of the sun. In this regard, the considered stress-energy tensor, and JHEP06(2023)055 consequently Einstein's equations of (2.10) all need to be altered and rewritten, because all subsequent calculations are no longer valid.…”

“…In this regard, the Hawking radiation cannot be neglected anymore, and the stress-energy tensor has another form, which must be written in its correct appearance. Even if the mass of the shell is smaller than a definite limit [62], then the Hawking radiation is so large and intense that the mass of the shell will be a function of time, which will lead to fundamental changes in the form of the equations and the results. The evaporation process leads to the disappearing of the trapped surface through the unification of the outer and inner horizons, resulting in an extremal black hole [63,64].…”