Spatially isotropic homogeneous spacetimes

Jose Figueroa-O'Farrill, Stefan Prohazka

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)1-77
Number of pages77
Journal Journal of High Energy Physics
Volume2019
Issue number1
DOIs
Publication statusPublished - 31 Jan 2019

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