Non-Relativistic Maxwell Chern-Simons Gravity

Abstract

We consider a non-relativistic (NR) limit of $(2+1)$-dimensional Maxwell Chern-Simons (CS) gravity with gauge algebra [Maxwell] $\oplus u(1)\oplus u(1)$. We obtain a finite NR CS gravity with a degenerate invariant bilinear form. We find two ways out of this difficulty: To consider i) [Maxwell] $\oplus u(1)$, which does not contain Extended Bargmann gravity (EBG); or, ii) the NR limit of [Maxwell] $\oplus u(1)\oplus u(1)\oplus u(1)$, which is a Maxwellian generalization of the EBG.

19 pages, 1 table, subsection 3.3 added, abstract and references modified