  In the framework of the conjectured duality relation between large $N$ gauge
theory and supergravity the spectra of masses in large $N$ gauge theory can be
determined by solving certain eigenvalue problems in supergravity. In this
paper we study the eigenmass problem given by Witten as a possible
approximation for masses in QCD without supersymmetry. We place a particular
emphasis on the treatment of the horizon and related boundary conditions. We
construct exact expressions for the analytic expansions of the wave functions
both at the horizon and at infinity and show that requiring smoothness at the
horizon and normalizability gives a well defined eigenvalue problem. We show
for example that there are no smooth solutions with vanishing derivative at the
horizon. The mass eigenvalues up to $m^{2}=1000$ corresponding to smooth
normalizable wave functions are presented. We comment on the relation of our
work with the results found in a recent paper by Cs\'aki et al.,
hep-th/9806021, which addresses the same problem.
