  We study the carrier relaxation dynamics in thin black phosphorus (bP) using
time-resolved differential transmission measurements. The inter-band and
intra-band transitions, relaxation, and carrier recombination lifetimes are
revealed by tuning the mid-infrared probe wavelength above and below the
bandgap of black phosphorus. When the probe energy exceeds the bandgap, Pauli
blocked inter-band transitions are observed. The differential transmission
signal changes sign from positive to negative when the probe energy is below
the bandgap, due to the absence of inter-band transitions and enhancement in
the free-carrier absorption (FCA). The minority carrier lifetime and radiative
recombination coefficient are estimated 1.3 ns, and 5.9$\rm \times 10^{-10}$
$\rm cm^{3}/s$, respectively. The overall recombination lifetime of bP is
limited by radiative recombination for excess carrier densities larger than
5$\rm \times 10^{19}$ $\rm cm^{-3}$.
