Vacuum Degeneracy and Conformal Mass in Lovelock AdS Gravity

TL;DR

This paper demonstrates that Conformal Mass can be defined in Lovelock AdS gravity theories for non-degenerate vacua, with conserved charges related to the Weyl tensor, but faces obstructions in degenerate vacua.

Contribution

It establishes a relation between Conformal Mass and vacuum degeneracy in Lovelock AdS gravity, clarifying when Conformal Mass can be consistently defined.

Findings

Conformal Mass is well-defined in non-degenerate Lovelock AdS vacua.

Conserved charges are proportional to the electric part of the Weyl tensor.

Vacuum degeneracy obstructs the definition of Conformal Mass.

Abstract

It is shown that the notion of Conformal Mass can be defined within a given anti-de Sitter (AdS) branch of a Lovelock gravity theory as long as the corresponding vacuum is not degenerate. Indeed, conserved charges obtained by the addition of Kounterterms to the bulk action turn out to be proportional to the electric part of the Weyl tensor, when the fall-off of a generic solution in that AdS branch is considered. The factor of proportionality is the degeneracy condition for the vacua in the particular Lovelock AdS theory under study. This last feature explains the obstruction to define Conformal Mass in the degenerate case.