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We consider a Compton cloud (CC) surrounding a black hole (BH) in anaccreting black hole system, where electrons propagate with thermal and bulkvelocities.In that cloud, soft (disk) photons may be upscattered off theseenergetic electrons and attain several MeV energies. They could then createpairs due to these photon-photon interactions. In this paper, we study theformation of the 511 keV annihilation line due to this photon-photoninteraction, which results in the creation of electron-positron pairs, followedby the annihilation of the created positrons with the CC electrons. Theappropriate conditions of annihilation line generation take place very close toa BH horizon within (10^3-10^4)m cm from it, where m is a BH hole mass in solarunits. As a result, the created annihilation line should be seen by the Earthobserver 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 experiencedby the created annihilation line photons when they emerge. This transientfeature should occur in any accreting black hole systems, Galactic orextragalactic. Observational evidences for this feature in several galacticblack hole systems is detailed in an accompanying paper (II). An extended hardtail of the spectrum up to 1 MeV may be also formed due to X-ray photonup-scattering off created pairs.

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