Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra

TL;DR

This paper explores a three-dimensional Chern-Simons gravity theory based on the Maxwell algebra, revealing an enlarged asymptotic symmetry algebra with three central charges and analyzing its physical implications.

Contribution

It introduces a novel boundary symmetry algebra for Maxwell-based gravity, extending the ms_3 algebra with Abelian generators and central charges, and studies its solutions and physical properties.

Findings

Boundary symmetry algebra is an extension of ms_3 with three central charges.

The theory's solutions include all geometries of General Relativity as special cases.

Vacuum energy and angular momentum are affected by the Maxwell field presence.

Abstract

We study a three-dimensional Chern-Simons gravity theory based on the Maxwell algebra. We find that the boundary dynamics is described by an enlargement and deformation of the $\mathfrak{bms}_3$ algebra with three independent central charges. This symmetry arises from a gravity action invariant under the local Maxwell group and is characterized by presence of Abelian generators which modify the commutation relations of the super-translations in the standard $\mathfrak{bms}_3$ algebra. Our analysis is based on the charge algebra of the theory in the BMS gauge, which includes the known solutions of standard asymptotically flat case. The field content of the theory is different than the one of General Relativity, but it includes all its geometries as particular solutions. In this line, we also study the stationary solutions of the theory in ADM form and we show that the vacuum energy and the vacuum angular momentum of the stationary configuration are influenced by the presence of the gravitational Maxwell field.