Asymptotic Black Holes and Conformal Mass in AdS Quadratic Curvature Gravity

TL;DR

This paper investigates conserved charges in Quadratic Curvature Gravity with AdS asymptotics, establishing a connection to conformal mass and analyzing the effects of criticality on charge linearization.

Contribution

It provides a detailed analysis of conserved charges in QCG, extending the concept of conformal mass to higher-curvature gravity and examining the impact of criticality conditions.

Findings

Conserved charges are proportional to the electric part of the Weyl tensor.

The extension of conformal mass to higher-curvature gravity is supported.

Criticality conditions obstruct charge linearization, unlike in Lovelock gravity.

Abstract

We explore the consistent truncation of conserved charges in Quadratic Curvature Gravity (QCG) with anti-de Sitter asymptotics to the linear order in the Weyl tensor. The QCG action is given by the most general curvature-squared corrections to Einstein gravity, and it is suitably rendered finite by the addition of extrinsic counterterms (Kounterterms). The conserved charges derived from this action are, as a consequence, nonlinear in the spacetime Riemann tensor. A detailed analysis of the falloff of generic static solutions leads to a charge proportional to the electric part of the Weyl tensor, without loss of information on the energy of the system. The procedure followed provides firmer ground to the extension of the notion of Conformal Mass to higher-curvature gravity, as it appears as associated to a renormalized action. We observe that criticality condition in QCG poses an obstruction to the charge linearization, in contrast to previous results in Lovelock gravity, where degeneracy condition plays a key role.