A Relation Between Gravity in $(3+1)$--Dimensions and Pontrjagin Topological Invariant

TL;DR

This paper explores a connection between a gravity theory in four dimensions and a topological invariant, which could shed light on transitioning from non-dynamical to dynamical gravity.

Contribution

It establishes a novel relation between MacDowell-Mansouri gravity and the Pontrjagin invariant, offering insights into dynamical gravity mechanisms.

Findings

Identifies a link between gravity and topological invariants.

Suggests a pathway for dynamical gravity development.

Provides theoretical groundwork for gravity-topology interplay.

Abstract

A relation between the MacDowell-Mansouri theory of gravity and the Pontrjagin toplogical invariant in $(3+1)$ dimensions is discussed. This relation may be of especial interest in the quest of finding a mechanism to go from non-dynamical to dynamical gravity.