  Gallium nitride (GaN) is a key semiconductor for solid-state lighting, but
its radiative processes are not fully understood. Here we show a
first-principles approach to accurately compute the radiative lifetimes in bulk
uniaxial crystals, focusing on wurtzite GaN. Our computed radiative lifetimes
are in very good agreement with experiment up to 100 K. We show that taking
into account excitons (through the Bethe-Salpeter equation) and spin-orbit
coupling to include the exciton fine structure is essential for computing
accurate radiative lifetimes. A model for exciton dissociation into free
carriers allows us to compute the radiative lifetimes up to room temperature.
Our work enables precise radiative lifetime calculations in III-nitrides and
other anisotropic solid-state emitters.
