Energy in Generic Higher Curvature Gravity Theories

TL;DR

This paper defines and calculates the energy in higher curvature gravity theories, revealing unique energy properties of specific models and analyzing their stability in various vacua.

Contribution

It introduces a method to compute energy in higher curvature theories and compares energy characteristics across different models, including Einstein-Gauss-Bonnet gravity.

Findings

Quadratic curvature models have distinct energy properties.

The traceless Ricci tensor squared model has zero energy.

Einstein-Gauss-Bonnet vacua are stable in flat and AdS spaces.

Abstract

We define and compute the energy of higher curvature gravity theories in arbitrary dimensions. Generically, these theories admit constant curvature vacua (even in the absence of an explicit cosmological constant), and asymptotically constant curvature solutions with non-trivial energy properties. For concreteness, we study quadratic curvature models in detail. Among them, the one whose action is the square of the traceless Ricci tensor always has zero energy, unlike conformal (Weyl) gravity. We also study the string-inspired Einstein-Gauss-Bonnet model and show that both its flat and Anti-de-Sitter vacua are stable.