### 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) |
---|---|

Article number | 175007 |

Journal | Classical and Quantum Gravity |

Volume | 35 |

Issue number | 17 |

DOIs | |

State | Published - Jul 27 2018 |

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### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Classical and Quantum Gravity*,

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

**Homogeneous nonrelativistic geometries as coset spaces.** / Grosvenor, Kevin T.; Hartong, Jelle; Keeler, Cynthia; Obers, Niels A.

Research output: Contribution to journal › Article

*Classical and Quantum Gravity*, vol. 35, no. 17, 175007. https://doi.org/10.1088/1361-6382/aad0f9

}

TY - JOUR

T1 - Homogeneous nonrelativistic geometries as coset spaces

AU - Grosvenor, Kevin T.

AU - Hartong, Jelle

AU - Keeler, Cynthia

AU - Obers, Niels A.

PY - 2018/7/27

Y1 - 2018/7/27

N2 - 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.

AB - 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.

KW - Bargmann algebra

KW - coset space

KW - Newton-Cartan geometry

KW - Newton-Hooke algebra

KW - Schrodinger algebra

UR - http://www.scopus.com/inward/record.url?scp=85051595225&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051595225&partnerID=8YFLogxK

U2 - 10.1088/1361-6382/aad0f9

DO - 10.1088/1361-6382/aad0f9

M3 - Article

AN - SCOPUS:85051595225

VL - 35

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 17

M1 - 175007

ER -