Mass in anti-de Sitter spaces

TL;DR

This paper discusses the use of boundary counterterms, including a finite phi^2 term, to accurately define mass in asymptotically anti-de Sitter spaces with matter fields, ensuring correct mass/charge relations.

Contribution

It introduces a finite counterterm proportional to phi^2 in the boundary stress tensor method for AdS spaces with matter, improving mass calculations.

Findings

Finite phi^2 counterterm is necessary for correct mass/charge relations.

The method applies to R-charged black holes in AdS_5.

Boundary stress tensor approach is validated with matter fields.

Abstract

The boundary stress tensor approach has proven extremely useful in defining mass and angular momentum in asymptotically anti-de Sitter spaces with CFT duals. An integral part of this method is the use of boundary counterterms to regulate the gravitational action and stress tensor. In addition to the standard gravitational counterterms, in the presence of matter we advocate the use of a finite counterterm proportional to phi^2 (in five dimensions). We demonstrate that this finite shift is necessary to properly reproduce the expected mass/charge relation for R-charged black holes in AdS_5.