Einstein gravity with generalized cosmological term from five-dimensional AdS-Maxwell-Chern-Simons gravity

TL;DR

This paper demonstrates how extended Einstein gravity theories with Maxwell and AdS-Maxwell symmetries can be derived from five-dimensional Chern-Simons actions via Randall-Sundrum compactification, linking to Horndeski scalar-tensor theories.

Contribution

It shows a novel derivation of extended Einstein gravities from five-dimensional Chern-Simons theories using compactification and contraction methods.

Findings

Extended 4D gravities are obtained from 5D Chern-Simons actions.

The contraction procedure connects different gauge algebra extensions.

Extended gravities are part of the Horndeski scalar-tensor family.

Abstract

Some time ago, the standard geometric framework of Einstein gravity was extended by gauging the Maxwell algebra as well as the so called AdS-Maxwell algebra. In this letter it is shown that the actions for these four-dimensional extended Einstein gravities can be obtained from the five-dimensional Chern-Simons gravities actions by using the Randall-Sundrum compactification procedure. It is found that the In\"on\"u-Wigner contraction procedure, in the Weimar-Woods sense, can be used both to obtain the Maxwell-Chern-Simons action from the AdS-Maxwell-Chern-Simons action and to obtain the Maxwell extension of Einstein gravity in 4D from the four-dimensional extended AdS-Maxwell-Einstein-Hilbert action. It is also shown that the extended four-dimensional gravities belongs to the Horndeski family of scalar-tensor theories.