Nonlinear Gravitational Lagrangians revisited

TL;DR

This paper extends the Legendre transformation approach to compare the dynamical content of nonlinear gravitational Lagrangians in metric and metric-affine frameworks, providing new insights into their differences.

Contribution

It generalizes a 1987 method to metric-affine models, offering a concise comparison of their dynamical structures.

Findings

Extended Legendre transformation to metric-affine models.

Clarified differences between metric and metric-affine formulations.

Provided a unified framework for analyzing nonlinear gravitational Lagrangians.

Abstract

The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.