  The hybrid perovskite CH3NH3PbI3 (MAPI) exhibits long minority-carrier
lifetimes and diffusion lengths. We show that slow recombination originates
from a spin-split indirect-gap. Large internal electric fields act on
spin-orbit-coupled band extrema, shifting band-edges to inequivalent
wavevectors, making the fundamental gap indirect. From a description of
photoluminescence within the quasiparticle self-consistent GW (QSGW)
approximation for MAPI, CdTe and GaAs, we predict carrier lifetime as a
function of light intensity and temperature. At operating conditions we find
radiative recombination in MAPI is reduced by a factor of more than 350
compared to direct gap behavior. The indirect gap is retained with dynamic
disorder.
