Abstract
We define energy () and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For , all purely quadratic models admit constant curvature vacua with arbitrary , and is the “cosmological” Abbott-Deser (AD) expression; instead, always vanishes in flat, , background. For combined Einstein-quadratic curvature systems without explicit -term vacuum must be flat space, and has the usual Arnowitt-Deser-Misner form. A -term forces unique de Sitter vacuum, with the sum of contributions from Einstein and quadratic parts to the AD form. We also discuss the effects on energy definition of higher curvature terms and of higher dimension.
- Received 30 May 2002
DOI:https://doi.org/10.1103/PhysRevLett.89.101101
©2002 American Physical Society