Homogeneous nonrelativistic geometries as coset spaces

We generalize the coset procedure of homogeneous spacetimes in (pseudo-)Riemannian geometry to non-Lorentzian geometries. These are manifolds endowed with nowhere vanishing invertible vielbeins that transform under local non-Lorentzian tangent space transformations. In particular we focus on symmetry algebras that give rise to (torsional) Newton–Cartan geometries, for which we demonstrate how the Newton–Cartan metric complex is determined by degenerate co- and contravariant symmetric bilinear forms on the coset. In specific cases we also show the connection of the resulting coset spacetimes to pseudo-Riemannian cosets via Inönü–Wigner contraction of relativistic algebras as well as null reduction. Our construction is of use for example when considering limits of the AdS/CFT correspondence in which spacetimes appear as gravitational backgrounds for string or gravity theories. (paper)