Thick domain walls and singular spaces

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. In all of these cases we can solve the equivalent quantum mechanics problem exactly, which provides the spectrum of graviton states on these spaces. 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.