  We discuss thick domain walls interpolating between spaces with naked
singularities and give arguments based on the $AdS$/CFT correspondence why such
singularities may be physically meaningful. Our examples include thick domain
walls with Minkowski, de Sitter, and anti-de Sitter geometries on the
four-dimensional slice. For flat domain walls we can solve the equivalent
quantum mechanics problem exactly, which provides the spectrum of graviton
states. In one of the examples we discuss, the continuum states have a mass
gap. We compare the graviton spectra with expectations from the $AdS$/CFT
correspondence and find qualitative agreement. We also discuss unitary boundary
conditions and show that they project out all continuum states.
