Black Hole Energy in Lovelock Unique Vacuum theories

TL;DR

This paper investigates defining black hole mass in Lovelock-AdS gravity theories using the Weyl tensor, revealing how vacuum degeneracy influences the energy formula and its truncation.

Contribution

It introduces a method to express black hole mass in Lovelock theories via the Weyl tensor, accounting for vacuum degeneracy levels.

Findings

Mass formula depends on vacuum degeneracy level k.

In maximally degenerate (Chern-Simons) case, the mass formula vanishes.

Vacuum energy is obtained from the polynomial curvature expression.

Abstract

In this thesis, we explore the possibility to define black hole mass in terms of the Weyl tensor for the entire family of Lovelock-AdS gravity theories. The level of degeneracy $k$ of the corresponding vacuum fixes the number of curvatures that should appear in the energy formula. Therefore, the charge expression which is a polynomial of maximal degree in the curvature, can be consistently truncated to an order $k$ in the Weyl tensor. In particular, for the maximally degenerate case in odd dimensions (Chern-Simons AdS) the expression identically vanishes and the mass must come from the formula that, in the other cases, produces the vacuum energy.