A new duality transformation for fourth-order gravity
Hans - Juergen Schmidt
TL;DR
This paper introduces a novel duality transformation for fourth-order gravity theories with Lagrangians depending on the Ricci scalar, establishing a conformal equivalence between dual Lagrangians through a new mathematical proof.
Contribution
It presents a new duality transformation for fourth-order gravity that leverages conformal invariance, expanding the mathematical tools available for analyzing such theories.
Findings
L and L are conformally equivalent for non-linear L(R)
The duality is established via conformal invariance of a specific differential operator
The proof introduces a new application of conformal invariance in gravity theories
Abstract
We prove that for non-linear L = L(R), the Lagrangians L and \hat L give conformally equivalent fourth-order field equations being dual to each other. The proof represents a new application of the fact that the operator <D'Alembertian minus R/6> is conformally invariant.
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