Mass in Lovelock Unique Vacuum gravity theories

Abstract

We derive an expression for conserved charges in Lovelock AdS gravity for solutions having $k$-fold degenerate vacua, making manifest a link between the degeneracy of a given vacuum and the nonlinearity of the energy formula. We show for a black hole solution to the field equations on a branch of multiplicity $k$ that its mass comes from an expression that contains the product of $k$ Weyl tensors. We prove that all divergent contributions of the type (Weyl)${}^q$, with $1\le q<k$, are suppressed. Our conserved charge definition is a natural generalization of the Conformal Mass by Ashtekar, Magnon and Das to the cases when $k>1$. Our results provide insight on the holographic properties of degenerate Lovelock theories.

arXiv comment27 pages, no figures; section 4.3 added; final version

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• Renormalized holographic entanglement entropy for Quadratic Curvature Gravity
• Higher-curvature generalization of Eguchi-Hanson spaces
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• Inhomogeneous metrics on complex bundles in Lovelock gravity
• A new formula for conserved charges of Lovelock gravity in AdS spacetimes and its generalization
• On the maximally symmetric vacua of generic Lovelock gravities
• An alternative study about the geometry and the first law of thermodynamics for AdS Lovelock gravity, using the definition of conserved charges
• A study about black hole solutions with nonconstant transversal curvature and its conserved charges in Lovelock gravity
• Thin shell dynamics in Lovelock gravity
• Scalar-hairy Lovelock gravity respects zeroth law