We study for the first time the environment of massive black hole (BH) seeds (similar to 10(4-5) M-circle dot) formed via the direct collapse of pristine gas clouds in massive haloes (>= 10(7) M-circle dot) at z > 6. Our model is based on the evolution of dark matter haloes within a cosmological N-body simulation, combined with prescriptions for the formation of BH along with both Population III (Pop III) and Population II (Pop II) stars. We calculate the spatially varying intensity of Lyman-Werner (LW) radiation from stars and identify the massive pristine haloes in which it is high enough to shut down molecular hydrogen cooling. In contrast to previous BH seeding models with a spatially constant LW background, we find that the intensity of LW radiation due to local sources, J(local), can be up to similar to 10(6) times the spatially averaged background in the simulated volume and exceeds the critical value, J(crit), for the complete suppression of molecular cooling, in some cases by four orders of magnitude. Even after accounting for possible metal pollution in a halo from previous episodes of star formation, we find a steady rise in the formation rate of direct collapse BHs (DCBHs) with decreasing redshift from 10(-3) Mpc(-3) z(-1) at z = 12 to 10(-2) Mpc(-3) z(-1) at z = 6. The onset of Pop II star formation at z approximate to 16 simultaneously marks the onset of the epoch of DCBH formation, as the increased level of LW radiation from Pop II stars is able to elevate the local levels of the LW intensity to J(local) > J(crit), while Pop III stars fail to do so at any time. The number density of DCBHs is sensitive to the number of LW photons and can vary by over an order of magnitude at z = 7 after accounting for reionization feedback. Haloes hosting DCBHs are more clustered than similar massive counterparts that do not host DCBHs, especially at redshifts z greater than or similar to 10. Also, the DCBHs that form at z > 10 are found to reside in highly clustered regions, whereas the DCBHs formed around z similar to 6 are more common. We also show that planned surveys with James Webb Space Telescope should be able to detect the supermassive stellar precursors of DCBHs.
