Towards non-AdS holography in 3-dimensional higher spin gravity

We take the first steps towards non-AdS holography in higher spin gravity. Namely, we propose a variational principle for generic 3-dimensional higher spin gravity that accommodates asymptotic backgrounds beyond AdS, like asymptotically Schrodinger, Lifshitz or warped AdS spacetimes. As examples we study in some detail the four sl(2) embeddings of spin-4 gravity and provide associated geometries, including an asymptotic Lifshitz black hole.