Electron-Positron pairs creation close to a black hole horizon. Red-shifted annihilation line in the emergent X-ray spectra of a black hole, part I

We consider a Compton cloud (CC) surrounding a black hole (BH) in an accreting black hole system, where electrons propagate with thermal and bulk velocities.In that cloud, soft (disk) photons may be upscattered off these energetic electrons and attain several MeV energies. They could then create pairs due to these photon-photon interactions. In this paper, we study the formation of the 511 keV annihilation line due to this photon-photon interaction, which results in the creation of electron-positron pairs, followed by the annihilation of the created positrons with the CC electrons. The appropriate conditions of annihilation line generation take place very close to a BH horizon within (10^3-10^4)m cm from it, where m is a BH hole mass in solar units. As a result, the created annihilation line should be seen by the Earth observer as a blackbody bump, or so called {reflection} bump at energies around (511/20) (20/z) keV where z~20 is a typical gravitational red-shift experienced by the created annihilation line photons when they emerge. This transient feature should occur in any accreting black hole systems, Galactic or extragalactic. Observational evidences for this feature in several galactic black hole systems is detailed in an accompanying paper (II). An extended hard tail of the spectrum up to 1 MeV may be also formed due to X-ray photon up-scattering off created pairs.