Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant

TL;DR

This paper develops a three-dimensional Maxwell Carroll gravity theory by taking the ultra-relativistic limit of Maxwell Chern-Simons gravity, introducing an extended symmetry to ensure a non-degenerate invariant tensor, and explores its relation to cosmological constant limits.

Contribution

It introduces an extended Maxwellian Carroll symmetry necessary for a non-degenerate invariant tensor, enabling the construction of a consistent Chern-Simons gravity theory with cosmological constant considerations.

Findings

Extended Maxwellian Carroll algebra with non-degenerate invariant tensor

Construction of Maxwell Carroll gravity as a flat limit of a cosmological constant theory

Identification of the algebra's origin as an ultra-relativistic limit

Abstract

In this work, we present the three-dimensional Maxwell Carroll gravity by considering the ultra-relativistic limit of the Maxwell Chern-Simons gravity theory defined in three spacetime dimensions. We show that an extension of the Maxwellian Carroll symmetry is necessary in order for the invariant tensor of the ultra-relativistic Maxwellian algebra to be non-degenerate. Consequently, we discuss the origin of the aforementioned algebra and theory as a flat limit. We show that the theoretical setup with cosmological constant yielding the extended Maxwellian Carroll Chern-Simons gravity in the vanishing cosmological constant limit is based on an enlarged extended version of the Carroll symmetry. Indeed, the latter exhibits a non-degenerate invariant tensor allowing the proper construction of a Chern-Simons gravity theory which reproduces the extended Maxwellian Carroll gravity in the flat limit.