Three-dimensional exotic Newtonian gravity with cosmological constant

TL;DR

This paper introduces a three-dimensional non-relativistic gravity theory with a cosmological constant by extending the exotic Newton-Hooke algebra, leading to a new algebra and a Chern-Simons action that generalizes extended Newtonian gravity.

Contribution

It constructs a novel exotic Newtonian algebra with a cosmological constant and derives a corresponding Chern-Simons gravity action, extending previous Newtonian frameworks.

Findings

The new algebra reproduces extended Newtonian gravity in the flat limit.

A Chern-Simons action for the exotic Newtonian algebra is formulated.

The theory generalizes non-relativistic gravity with a cosmological constant.

Abstract

In this work we introduce a cosmological constant in the extended Newtonian gravity theory. To this end, we extend the exotic Newton-Hooke algebra by introducing new generators and central charges. The new algebra obtained here has been denoted as exotic Newtonian algebra and reproduces the extended Newtonian one in the flat limit $\ell\rightarrow\infty$. A three-dimensional Chern-Simons action for the exotic Newtonian algebra is presented. We show that the non-relativistic gravity theory proposed here reproduces the most general extended Newtonian gravity theory in the flat limit.