Quadratic Curvature Correction to the Euclidean Action of Rotating AdS Black Holes in General Dimensions

TL;DR

This paper computes the first-order quadratic curvature corrections to the Euclidean action of rotating AdS black holes in arbitrary dimensions, enhancing understanding of their thermodynamic properties.

Contribution

It introduces a perturbative method to calculate quadratic curvature corrections to the Euclidean action of rotating AdS black holes in any dimension.

Findings

Derived the corrected Euclidean action incorporating quadratic curvature invariants.

Expressed the Gibbs free energy as a function of temperature and angular velocities.

Provided insights into the thermodynamics of corrected black hole solutions.

Abstract

We adopt the improved Reall-Santos method to obtain the leading-order perturbative correction of the quadratic curvature invariants to the on-shell Euclidean action of rotating anti-de Sitter (AdS) black holes in general $D$ dimensions. The corresponding Gibbs free energy is a function of thermodynamic variables, temperature and angular velocities, which are unperturbed in this approach.