Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes

Understand

Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions.

• In this paper, we continue the study of these "maximally symmetric" spacetimes by investigating their local geometry.
• For each such spacetime and relative to exponential coordinates, we calculate the (infinitesimal) action of the kinematical symmetries, paying particular attention to the action of the boosts, showing in almost all cases that they act with generic non-compact orbits.
• We also calculate the soldering form, the associated vielbein and any invariant aristotelian, galilean or carrollian structures.