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] ⊕ u(1) ⊕ 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] ⊕ u(1), which does not contain Extended Bargmann gravity (EBG); or, ii) the NR limit of [Maxwell] ⊕ u(1)⊕u(1)⊕u(1), which is a Maxwellian generalization of the EBG.