Vacuum Degeneracy and Conformal Mass in Lovelock AdS Gravity

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.

arXiv comment22 pages, no figures, a few references added

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• Renormalized holographic entanglement entropy for Quadratic Curvature Gravity
• Topological invariants and the definition of energy in quadratic gravity theory
• Quasi-local energy and ADM mass in pure Lovelock gravity
• Field-theoretical construction of currents and superpotentials in Lovelock gravity
• Inhomogeneous metrics on complex bundles in Lovelock gravity
• A new formula for conserved charges of Lovelock gravity in AdS spacetimes and its generalization
• Conserved quantities for black hole solutions in pure Lovelock gravity
• A study about black hole solutions with nonconstant transversal curvature and its conserved charges in Lovelock gravity
• Thin shell dynamics in Lovelock gravity