Brief Note on AMD Conserved Quantities in Quadratic Curvature Theories

TL;DR

This paper revisits AMD conserved quantities in quadratic curvature theories, correcting previous errors and aligning the conformal mass definition with critical gravity results, especially regarding black hole mass in asymptotically AdS spacetimes.

Contribution

It corrects an earlier error in the AMD approach and demonstrates its consistency with Deser and Tekin's methods in critical gravity.

Findings

Corrected the AMD conformal mass calculation.

Confirmed zero mass for black holes in critical gravity.

Aligned AMD results with Deser and Tekin's findings.

Abstract

Motivated by the recent work on critical gravity theories in dimensions D>3, we reexamine the results in [arXiv:hep-th/0501044], where the conformal mass definition of Ashtekar, Magnon and Das (AMD) for asymptotically AdS space-times was generalized to incorporate curvature squared terms. The results in [arXiv:hep-th/0501044] appear to contradict the findings in critical gravity, where, using the methods of Deser and Tekin, black holes were shown to have zero mass. We show that after correcting an error in [arXiv:hep-th/0501044], the AMD approach actually produces results in complete agreement with those obtained by using the methods of Deser and Tekin.