# Mass in Lovelock Unique Vacuum gravity theories

## TL;DR

This paper derives a generalized conserved charge expression for Lovelock AdS gravity solutions with degenerate vacua, linking vacuum degeneracy to energy nonlinearity and extending the Conformal Mass concept.

## Contribution

It introduces a new conserved charge formula for Lovelock gravity with degenerate vacua, revealing the relation between vacuum degeneracy and energy nonlinearity, and extends the Conformal Mass to these cases.

## Key findings

- Mass involves a product of k Weyl tensors for solutions on a k-fold degenerate vacuum.
- Divergent terms with (Weyl)^q for q<k are suppressed.
- Provides holographic insights into degenerate Lovelock 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.