Quadratic curvature corrections to 5-dimensional Kerr-AdS black hole thermodynamics by background subtraction method

TL;DR

The paper demonstrates that the background subtraction method is applicable to five-dimensional Kerr–AdS spacetimes, even when higher-derivative (quadratic-curvature) corrections are present. It provides a rigorous criterion for applicability, verifies finiteness of reference-subtracted charges, and computes the first-order corrected Gibbs free energy, finding exact agreement with results from holographic renormalization. This equivalence substantiates the background subtraction approach as a simpler yet reliable tool for black hole thermodynamics in AdS with higher-derivative gravity. The work also clarifies that one need not solve the full corrected metric to obtain thermodynamic quantities, and it points toward future exploration of higher-order corrections and more general scenarios.

Abstract

We justify the applicability of the background subtraction method to both Einstein's gravity and its higher derivative corrections in 5-dimensional asymptotically AdS spacetimes, where the corresponding higher derivative corrections to the expression for the ADM mass and angular momentum are also worked out. Then we further apply the background subtraction method to calculate the first order corrected Gibbs free energy by the quadratic curvature terms for the 5-dimensional Kerr-AdS black hole, which is in exact agreement with the previous result obtained by the holographic renormalization method. Such an agreement in turn substantiates the applicability of the background subtraction method.