Spatially isotropic homogeneous spacetimes

Abstract

We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\ge 0$. 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.

51 pages, 6 figures, 17 tables. Updated references and corrected an inconsequential error in Section 4.2.5

References in corpus (13)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Newtonian Gravity and the Bargmann Algebra
• Spacetime Symmetries of the Quantum Hall Effect
• A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
• Galilean Conformal Electrodynamics
• Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra
• General coordinate invariance in quantum many-body systems
• Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
• Aging and Holography
• Metrics with Galilean Conformal Isometry

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