  We present results for a numerical study of the ghost propagator in Coulomb
gauge whereby lattice results for the spatial gluon propagator are used as
input to solving the ghost Dyson-Schwinger equation. We show that in order to
solve completely, the ghost equation must be supplemented by a boundary
condition (the value of the inverse ghost propagator dressing function at zero
momentum) which determines if the solution is critical (zero value for the
boundary condition) or subcritical (finite value). The various solutions
exhibit a characteristic behavior where all curves follow the same (critical)
solution when going from high to low momenta until `forced' to freeze out in
the infrared to the value of the boundary condition. The boundary condition can
be interpreted in terms of the Gribov gauge-fixing ambiguity; we also
demonstrate that this is not connected to the renormalization. Further, the
connection to the temporal gluon propagator and the infrared slavery picture of
confinement is discussed.
