Weak field limit in vierbein-Einstein-Palatini formalism and Fierz-Pauli Equation

TL;DR

This paper explores the weak field limit of gravity within the vierbein-Einstein-Palatini formalism, deriving perturbation equations and comparing them to metric perturbations, while also formulating Fierz-Pauli equations for massive gravitons.

Contribution

It introduces a novel formulation of gravitational perturbations in the vierbein-Einstein-Palatini formalism and extends Fierz-Pauli equations to arbitrary curved backgrounds.

Findings

Derived perturbation equations around arbitrary backgrounds

Compared vierbein and metric perturbation formalisms

Formulated Fierz-Pauli equations for massive gravitons

Abstract

We consider the weak field limit of gravity in the vierbein-Einstein-Palatini formalism, find the action and the equations for perturbations around an arbitrary background, and compare them with the usual metric perturbation equations. We also write the Fierz-Pauli equations for massive gravitons on an arbitrary curved background in this formalism.