Nonlinear Supergravity on a Brane without Compactification

We show that smooth domain wall spacetimes supported by a scalar field separating two anti–de Sitter–like regions admit a single graviton bound state. Our analysis yields a fully nonlinear supergravity treatment of the Randall-Sundrum model. Our solutions describe a $\mathrm{pp}$-wave propagating in the domain wall background spacetime. If the latter is a Bogomol'nyi-Prasad-Sommerfeld state, our solutions retain some supersymmetry. Nevertheless, the Kaluza-Klein modes generate “ $\mathrm{pp}$ curvature” singularities in the bulk located where the horizon of the anti–de Sitter region would ordinarily be.