Extremal Kerr black hole/CFT correspondence in the five dimensional Gödel universe

TL;DR

The paper investigates the microscopic origin of entropy for five-dimensional extremal black holes in a Gödel universe by applying the Kerr/CFT correspondence to both the extremal Kerr-Gödel and extremal charged Kerr-Gödel solutions. Using near-horizon geometries in the Bardeen-Horowitz sense, it identifies two boundary-preserving diffeomorphisms that generate dual chiral Virasoro algebras, and computes their central charges and Frolov-Thorne temperatures. The Cardy formula then yields microscopic entropies that precisely reproduce the Bekenstein-Hawking entropies for both cases, providing a nontrivial check of the duality. The results demonstrate the robustness of Kerr/CFT in nontrivial higher-dimensional backgrounds and connect to known limits such as BMPV.

Abstract

We extend the method of Kerr/CFT correspondence recently proposed in arXiv:0809.4266 [hep-th] to the extremal (charged) Kerr black hole embedded in the five-dimensional Gödel universe. With the aid of the central charges in the Virasoro algebra and the Frolov-Thorne temperatures, together with the use of the Cardy formula, we have obtained the microscopic entropies that precisely agree with the ones macroscopically calculated by Bekenstein-Hawking area law.