Three-dimensional Maxwellian Extended Newtonian gravity and flat limit

TL;DR

This paper introduces new three-dimensional Maxwellian extended Newtonian gravity models, including cosmological constant effects, derived via non-relativistic limits and algebra expansion methods, expanding the understanding of non-relativistic gravity theories.

Contribution

It presents a novel Maxwellian version of extended Newtonian gravity and explores its cosmological constant extension using algebra expansion techniques.

Findings

Maxwellian extended Newtonian gravity derived as a non-relativistic limit.

Inclusion of cosmological constant in the Maxwellian framework.

Application of semigroup expansion method to algebraic structures.

Abstract

In the present work we find novel Newtonian gravity models in three spacetime dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular $U(1)$-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.