Homogeneous nonrelativistic geometries as coset spaces

Kevin T. Grosvenor, Jelle Hartong, Cynthia Keeler, Niels A. Obers

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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 languageEnglish (US)
Article number175007
JournalClassical and Quantum Gravity
Issue number17
StatePublished - Jul 27 2018


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

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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