Energy in Fourth Order Gravity

TL;DR

This paper investigates the concept of energy in fourth-order gravity theories derived from quadratic Lagrangians, providing examples, interpretations, and positive energy theorems within specific contexts.

Contribution

It offers a detailed analysis of energy conservation principles in fourth-order gravitational theories and introduces new approaches to understanding and studying energy in these models.

Findings

Examples illustrating the notion of energy in these theories

Interpretations that aid understanding of energy concepts

Positive energy theorems established in restricted cases

Abstract

In this paper we make a detailed analysis of conservation principles in the context of a family of fourth-order gravitational theories generated via a quadratic Lagrangian. In particular, we focus on the associated notion of energy and start a program related to its study. We also exhibit examples of solutions which provide intuitions about this notion of energy which allows us to interpret it, and introduce several study cases where its analysis seems tractable. Finally, positive energy theorems are presented in restricted situations.