Non-Relativistic Maxwell Chern-Simons Gravity

TL;DR

This paper explores non-relativistic limits of (2+1)-dimensional Maxwell Chern-Simons gravity, resulting in two different theories: one excluding Extended Bargmann gravity and another as a Maxwellian extension of it.

Contribution

It introduces two novel non-relativistic Maxwell Chern-Simons gravity theories derived from different gauge algebra limits.

Findings

Obtained a finite non-relativistic CS gravity with a degenerate bilinear form.

Identified two approaches: one excluding EBG, another as a Maxwellian extension of EBG.

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.