Conserved Charges in Extended Theories of Gravity

TL;DR

This paper reviews the construction of conserved charges in extended gravity theories, analyzing various methods and their properties in different spacetime backgrounds, with implications for black hole entropy.

Contribution

It provides a comprehensive review of conserved charge constructions in extended gravity, including explicit computations and discussions of gauge invariance and quasi-local definitions.

Findings

Explicit calculations of conserved charges in various gravity theories.

Analysis of gauge transformations and their effects on charges.

Discussion of conserved charges' relevance to black hole entropy.

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.