### Abstract

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 nonrelativistic 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 nonrelativistic coset spacetimes to pseudo-Riemannian cosets via Inonu-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 nonrelativistic spacetimes appear as gravitational backgrounds for nonrelativistic string or gravity theories.

Original language | English (US) |
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Article number | 175007 |

Journal | Classical and Quantum Gravity |

Volume | 35 |

Issue number | 17 |

DOIs | |

State | Published - Jul 27 2018 |

### Keywords

- Bargmann algebra
- Newton-Cartan geometry
- Newton-Hooke algebra
- Schrodinger algebra
- coset space

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

*Classical and Quantum Gravity*,

*35*(17), [175007]. https://doi.org/10.1088/1361-6382/aad0f9