Generalized Einstein gravities and generalized AdS symmetries

TL;DR

This paper constructs generalized four-dimensional gravity theories based on extended AdS symmetries, demonstrating how Einstein gravity can be extended and contracted using algebraic methods involving gauge connections and algebra extensions.

Contribution

It introduces a framework for extending Einstein gravity via generalized AdS symmetries and shows how these extensions relate through contraction methods.

Findings

Derived a generalized gravity action from AdSL4 gauge connections.

Showed how Einstein gravity extends to Maxwell and B5 symmetries.

Demonstrated contraction procedures connecting extended and standard gravity theories.

Abstract

We consider the curvatures 2 form asociated with AdSL4 valued one-form gauge connetion, and then we construct a four-dimensional action that generalize the Einstein-Hilbert gravity. It is shown that the Maxwell extension of Einstein gravity can be obtained from AdSL4-gravity making use of the Inonu-Wigner contraction method. In the same way, by gauging the AdSL5 spacetime algebra, the Einstein-Hilbert gravity is extended including the vector fields kab and ha which are associated with non-Abelian tensors and non Abelian vectors charges in the AdSL5 algebra. The B5 extension of Einstein gravity can be obtained from AdSL5 gravity using of the above mentioned contraction procedure. Some aspects of a gravity based on the algebra AdSL6 are considered in an appendix.