The Exterior Calculus of Quadratic Gravity

TL;DR

This paper derives the field equations for quadratic curvature gravity in four dimensions using exterior calculus, and formulates their linearized version through perturbation forms, providing a geometric framework for such theories.

Contribution

It introduces a novel exterior calculus approach to derive and linearize quadratic gravity field equations, enhancing geometric understanding.

Findings

Derived metric field equations using exterior calculus

Formulated linearized equations with perturbation forms

Provides a geometric framework for quadratic gravity

Abstract

The metric tensor field equations for the general quadratic curvature gravity in four spacetime dimensions are derived by making use of the algebra of the exterior forms defined on pseudo-Riemannian manifolds and the identities satisfied by the Riemann curvature tensor. The linearized metric field equations are formulated in terms of perturbation 1-form fields.