  Nucleon-antinucleon annihilation in the large $N_c$ limit of QCD in the
Witten regime of fixed velocity is considered with a focus on the spin and
isospin dependence of the annihilation cross-section. In general, time-reversal
and isospin invariance restricts the annihilation cross-section to depend on 6
independent energy-dependent terms. At large $N_c$, a spin-flavor symmetry
emerges in the theory that acts to further restrict the dependence of the
annihilation cross-section to three of these terms; the other terms amount to
$1/N_c$ corrections. Assuming dominance of the leading order terms, several
identities are derived that relate annihilation in different spin-isospin
channels. A key prediction is that for unpolarized nucleons in Witten
kinematics, the proton-antiproton annihilation cross-section should be equal to
the proton-antineutron annihilation cross-section up to corrections of relative
order $1/N_c$. Unpolarized nucleon-antinucleon annihilation data appears to be
consistent with this expectation.
