Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension
Abstract
We extend a recent classification of three-dimensional spatially isotropic homogeneous spacetimes to Chern--Simons theories as three-dimensional gravity theories on these spacetimes. By this we find gravitational theories for all carrollian, galilean, and aristotelian counterparts of the lorentzian theories. In order to define a nondegenerate bilinear form for each of the theories, we introduce (not necessarily central) extensions of the original kinematical algebras. Using the structure of so-called double extensions, this can be done systematically. For homogeneous spaces that arise as a limit of (anti-)de Sitter spacetime, we show that it is possible to take the limit on the level of the action, after an appropriate extension. We extend our systematic construction of nondegenerate bilinear forms also to all higher-dimensional kinematical algebras.
Keywords
Cite
@article{arxiv.1903.09165,
title = {Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension},
author = {Javier Matulich and Stefan Prohazka and Jakob Salzer},
journal= {arXiv preprint arXiv:1903.09165},
year = {2019}
}
Comments
52 pages, 2 figures, 11 tables; v2: matches published version, additional references added and incorporated referee suggestions