New Energy Definition for Higher Curvature Gravities

TL;DR

This paper introduces a new way to define conserved quantities in higher curvature gravity theories that overcomes limitations of traditional methods, especially in flat backgrounds and complex curvature models.

Contribution

It presents a curvature-based conserved quantity definition for higher derivative gravity models, improving upon existing energy concepts and correctly distinguishing different curvature actions in higher dimensions.

Findings

Correctly discriminates between Gauss-Bonnet and generic higher derivative actions in D>4.

Avoids zero energy theorems and issues in flat backgrounds.

Provides a natural and robust definition based on curvature asymptotics.

Abstract

We propose a novel but natural definition of conserved quantities for gravity models quadratic and higher in curvature. Based on the spatial asymptotics of curvature rather than of metric, it avoids the GR energy machinery's more egregious problems--such as zero energy "theorems" and failure in flat backgrounds -- in this fourth-derivative realm. In D>4, the present expression indeed correctly discriminates between second derivative Gauss-Bonnet and generic, fourth derivative, actions.