Vacuum Degeneracy and Conformal Mass in Lovelock AdS Gravity

Understand

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.