Warped Ricci-flat reductions

We present a simple class of warped-product vacuum (Ricci-flat) solutions to ten- and eleven-dimensional supergravity, where the internal space is flat and noncompact and the warp factor supports de Sitter (dS) and anti-de Sitter (AdS) vacua, in addition to trivial Minkowski vacua with compact internal spaces. We outline the construction of consistent Kaluza-Klein reductions and show that, although our vacuum solutions are nonsupersymmetric, these are closely related to the bosonic part of well-known maximally supersymmetric reductions on spheres. We comment on the stability of our solutions, noting that (A)dS3 vacua pass routine stability tests.