Energy in Generic Higher Curvature Gravity Theories

TL;DR

The paper develops a gauge-invariant, surface-charge formalism to define and compute energy for generic higher-curvature gravity theories in arbitrary dimensions, focusing on asymptotically constant-curvature spacetimes. It derives a general Killing-charge expression for quadratic gravities, then specializes to the string-inspired Einstein–Gauss–Bonnet model to show positive energy for external solutions and stability of AdS vacua. A key result is the identification of a unique purely quadratic theory with zero energy for all constant-curvature backgrounds, while adding an Einstein term destroys this property. The framework generalizes Abbott–Deser charges to higher-order terms and provides a foundation for analyzing vacuum stability and global charges in string-inspired and higher-derivative gravity theories.

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.