Conserved Charges in Extended Theories of Gravity

Abstract

We give a detailed review of construction of conserved quantities in extended theories of gravity for asymptotically maximally symmetric spacetimes and carry out explicit computations for various solutions. Our construction is based on the Killing charge method, and a proper discussion of the conserved charges of extended gravity theories with this method requires studying the corresponding charges in Einstein's theory with or without a cosmological constant. Hence we study the ADM charges (in the asymptotically flat case but in generic viable coordinates), the AD charges (in generic Einstein spaces, including the anti-de Sitter spacetimes) and the ADT charges in anti-de Sitter spacetimes. We also discuss the conformal properties and the behavior of these charges under large gauge transformations as well as the linearization instability issue which explains the vanishing charge problem for some particular extended theories. We devote a long discussion to the quasi-local and off-shell generalization of conserved charges in the 2+1 dimensional Chern-Simons like theories and suggest their possible relevance to the entropy of black holes.

arXiv comment116 pages, 1 figure, a review, references added, matches the version to appear in Physics Reports

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• A Systematic Construction of Kastor-Traschen Currents and their Extensions to Generic Powers of Curvature
• Energy in Fourth Order Gravity
• Conserved charges and asymptotic symmetries of BTZ-like black holes in Einstein-bumblebee gravity
• Generalized Off-Shell ADT Conserved Charges in the Presence of Matter Chern-Simons Term
• Extended Near Horizon Symmetries of Extremal BTZ Black Holes in 3D Massive Gravity
• The Exterior Calculus of Quadratic Gravity
• A note on the pp-wave solution of Minimal Massive 3D Gravity coupled with Maxwell-Chern-Simons theory
• Off-Shell ADT Conserved Quantities in Palatini Gravity