Higher derivative corrections to Kerr-AdS black hole thermodynamics

TL;DR

Addresses first-order thermodynamic corrections to Kerr-AdS black holes induced by higher-derivative gravity terms up to cubic in the Riemann tensor. Uses the background subtraction method justified by covariant phase-space arguments and a decomposition trick that shifts the AdS radius to $l_e$ and splits the bulk action into an effective Einstein-Hilbert part plus a residual higher-derivative contribution. Derives explicit corrections to the Gibbs free energy $G$, entropy $S$, angular momentum $J$, and mass $M$ in the grand canonical ensemble, and cross-validates results against the Lorentzian ADM and Wald formulas, including a Gauss-Bonnet check. Demonstrates robustness of the approach and outlines extensions to higher dimensions and to more general higher-derivative terms.

Abstract

Instead of the much more involved covariant counterterm method, we apply the well justified background subtraction method to calculate the first order corrections to Kerr-AdS black hole thermodynamics induced by the higher derivative terms up to the cubic of Riemann tensor, where the computation is further simplified by the decomposition trick for the bulk action. The validity of our results is further substantiated by examining the corrections induced by the Gauss-Bonnet term. Moreover, by comparing our results with those obtained via the ADM and Wald formulas in Lorentzian signature, we can extract some generic information about the first order corrected black hole solution induced by each higher derivative term.