Geometrical description of spin-2 fields

TL;DR

This paper proposes a novel geometric framework where torsion in Cartan geometry corresponds to two spin-2 fields, offering an alternative to traditional General Relativity for describing such fields.

Contribution

It introduces a new approach linking torsion in Cartan geometry to spin-2 fields, expanding the geometrization of these fields beyond Einstein's theory.

Findings

Torsion can be associated with two spin-2 fields in Cartan geometry.

A Hilbert-Einstein Lagrangian is used to generate dynamics for these fields.

The approach offers an alternative to traditional geometrization of spin-2 fields.

Abstract

We show that the torsion of a Cartan geometry can be associated to two spin-2 fields. This structure allows a new approach to deal with the proposal of geometrization of spin-2 fields besides the traditional one dealt with in General Relativity. We use the associated Hilbert-Einstein Lagrangian $R$ for generating a dynamics for the fields.