The need to construct a fermion quantum field theory in

black-hole spacetimes is an acute one. The study of

gravitational collapse necessitates the need of such. In

this dissertation, we construct the theory of free fermions

living on the static Schwarzschild black-hole and the

rotating Kerr black-hole. The construction capitalises

upon the fact that both black-holes are stationary

axisymmetric solutions to Einstein's equation. A

factorisability ansatz is developed whereby simple

quantum modes can be found, for such stationary

spacetimes with azimuthal symmetry. These modes are

then employed for the purposes of a canonical

quantisation of the corresponding fermionic theory. At

the same time, we suggest that it may be impossible to

extend a quantum field theory continuously across an

event horizon. This split of a quantum field theory ensures

the thermal character of the Hawking radiation. In our

case, we compute and prove that the spectrum of

neutrinos emitted from a black-hole via the Hawking

process is indeed thermal. We also study fermion

scattering amplitudes off the Schwarzschild black-hole.