Conformal mass in Einstein-Gauss-Bonnet AdS gravity

TL;DR

This paper extends the conformal mass definition to Einstein-Gauss-Bonnet AdS gravity, showing conserved charges are encoded in the Weyl tensor's electric part and aligning Kounterterm and AMD charges under certain conditions.

Contribution

It generalizes the conformal mass concept to a gravity theory with Gauss-Bonnet terms using Kounterterms and Weyl tensor analysis.

Findings

Kounterterm charges and AMD charges agree under specific asymptotic conditions

Conserved charges are encoded in the electric part of the Weyl tensor

The method applies to any dimension with the same fall-off behavior

Abstract

In this paper, we show that the physical information given by conserved charges for asymptotically AdS spacetimes in Einstein-Gauss-Bonnet AdS gravity is encoded in the electric part of the Weyl tensor. This result generalizes the conformal mass definition by Ashtekar-Magnon-Das (AMD) to a gravity theory with a Gauss-Bonnet term. This proof makes use of the Noether charges obtained from an action renormalized by the addition of counterterms which depend on the extrinsic curvature (Kounterterms). If the asymptotic fall-off behaviour of the Weyl tensor is same as the one considered in the AMD method, then the Kounterterm charges and the AMD charges agree in any dimension.