  We consider the bound-state energy levels of a spin-1/2 fermion in the
gravitational field of a near-black hole object. In the limit that the metric
of the body becomes singular, all binding energies tend to the rest-mass energy
(i.e. total energy approaches zero). We present calculations of the ground
state energy for three specific interior metrics (Florides, Soffel and
Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in
the singular metric limit. The lack of zero or negative energy states prior to
this limit being reached prevents particle pair production occurring.
Therefore, in contrast to the Coulomb case, no pairs are produced in the
non-singular static metric. For the Florides and Soffel metrics the singularity
occurs in the black hole limit, while for the Schwarzschild interior metric it
corresponds to infinite pressure at the centre. The behaviour of the energy
level spectrum is discussed in the context of the semi-classical approximation
and using general properties of the metric.
