Magnetic Mass in 4D AdS Gravity

TL;DR

This paper derives a covariant expression for charges in 4D AdS gravity with topological terms, showing that magnetic mass equals the Ashtekar-Magnon-Das definition for self-dual solutions.

Contribution

It introduces a fully covariant formula for diffeomorphic charges in 4D AdS gravity including topological invariants, linking magnetic mass to known definitions in self-dual cases.

Findings

Charge expression accounts for Gauss-Bonnet and Pontryagin terms.

Action is stationary for (anti) self-dual Weyl tensor solutions.

Magnetic mass equals Ashtekar-Magnon-Das charge for self-dual configurations.

Abstract

We provide a fully-covariant expression for the diffeomorphic charge in 4D anti-de Sitter gravity, when the Gauss-Bonnet and Pontryagin terms are added to the action. The couplings of these topological invariants are such that the Weyl tensor and its dual appear in the on-shell variation of the action, and such that the action is stationary for asymptotic (anti) self-dual solutions in the Weyl tensor. In analogy with Euclidean electromagnetism, whenever the self-duality condition is global, both the action and the total charge are identically vanishing. Therefore, for such configurations the magnetic mass equals the Ashtekhar-Magnon-Das definition.