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Journal of High Energy Physics

, 2019:229 | Cite as

Spatially isotropic homogeneous spacetimes

  • José Figueroa-O’FarrillEmail author
  • Stefan Prohazka
Open Access
Regular Article - Theoretical Physics
  • 22 Downloads

Abstract

We classify simply-connected homogeneous (D +1)-dimensional spacetimes for kinematical and aristotelian Lie groups with D-dimensional space isotropy for all D ≥ 0. Besides well-known spacetimes like Minkowski and (anti) de Sitter we find several new classes of geometries, some of which exist only for D = 1, 2. These geometries share the same amount of symmetry (spatial rotations, boosts and spatio-temporal translations) as the maximally symmetric spacetimes, but unlike them they do not necessarily admit an invariant metric. We determine the possible limits between the spacetimes and interpret them in terms of contractions of the corresponding transitive Lie algebras. We investigate geometrical properties of the spacetimes such as whether they are reductive or symmetric as well as the existence of invariant structures (riemannian, lorentzian, galilean, carrollian, aristotelian) and, when appropriate, discuss the torsion and curvature of the canonical invariant connection as a means of characterising the different spacetimes.

Keywords

Space-Time Symmetries Differential and Algebraic Geometry 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Maxwell Institute and School of MathematicsThe University of EdinburghEdinburghU.K.
  2. 2.Université Libre de Bruxelles and International Solvay Institutes, Physique Mathématique des Interactions FondamentalesBruxellesBelgium

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