  We present theoretical analysis and first-principles calculation of the
radiative lifetime of excitons in semiconducting carbon nanotubes. An intrinsic
lifetime of the order of 10 ps is computed for the lowest optically active
bright excitons. The intrinsic lifetime is however a rapid increasing function
of the exciton momentum. Moreover, the electronic structure of the nanotubes
dictates the existence of dark excitons nearby in energy to each bright
exciton. Both effects strongly influence measured lifetime. Assuming a thermal
occupation of bright and dark exciton bands, we find an effective lifetime of
the order of 10 ns at room temperature, in good accord with recent experiments.
