  The version of the warp model that we proposed to explain the mass scale
hierarchy has been extended by the introduction of one or more singularities in
the metric. We restricted ourselves to a real massless scalar field supposed to
propagate in a five dimensional bulk with the extradimension being compactified
on a strip or on a circle. With the same emphasis on the hermiticity and
commutativity properties of the Kakuza Klein operators, we have established all
the allowed boundary conditions to be imposed on the fields. From them, for
given positions of the singularities, one can deduce either mass eigenvalues
building up a Kaluza Klein tower, or a tachyon, or a zero mass state. Assuming
the Planck mass to be the high mass scale and by a choice, unique for all
boundary conditions, of the major warp parameters, the low lying mass
eigenvalues are of the order of the TeV, in this way explaining the mass scale
hierarchy. In our model, the physical masses are related to the Kaluza Klein
eigenvalues, depending on the location of the physical brane which is an
arbitrary parameter of the model. Illustrative numerical calculations are given
to visualize the structure of Kaluza Klein mass eigenvalue towers. Observation
at high energy colliders like LHC of a mass tower with its characteristic
structure would be the fingerprint of the model.
