Energy of anti-de Sitter black holes in odd-dimensional Quadratic Curvature Gravity

TL;DR

This paper introduces a method to accurately compute the energy of black holes in odd-dimensional Anti-de Sitter spaces within Quadratic Curvature Gravity, using extrinsic counterterms to ensure finite, background-independent results.

Contribution

It develops new formulas employing Kounterterms for calculating black hole energy in QCG without background subtraction or linearization.

Findings

Successfully reproduces black hole energy without background subtraction.

Provides finite, well-defined energy formulas in odd-dimensional AdS spaces.

Compatible with asymptotically AdS boundary conditions in QCG.

Abstract

We provide new formulas for the energy of black hole solutions in the anti-de Sitter (AdS) sector of a generic gravity theory with curvature-squared terms. This is achieved by the addition of counterterms of the extrinsic type (\emph{Kounterterms}) which produces a finite variation of the total action. The procedure is compatible with the boundary conditions in asymptotically AdS spaces within the framework of Quadratic Curvature Gravity (QCG) theory. As a consequence, without resorting to background-substraction, or linearized methods, the conserved charges correctly reproduce the energy of static black holes in QCG.