Notes on Five-dimensional Kerr Black Holes

TL;DR

This paper explores the geometry of five-dimensional Kerr black holes, introducing new spacetime models and demonstrating the integrability of geodesics in AdS Kerr black holes, revealing their spectral similarities to Ricci-flat Kerr black holes.

Contribution

It presents a detailed geometric analysis of five-dimensional Kerr black holes, including the introduction of Kerr-Star, Star-Kerr, and Kruskal spaces, and shows the integrability and spectral properties of AdS Kerr black holes.

Findings

Geodesics of AdS Kerr black holes are integrable.

Five-dimensional AdS Kerr black holes are isospectrum deformations of Ricci-flat Kerr black holes.

New spacetime models (Kerr-Star, Star-Kerr, Kruskal) are introduced.

Abstract

The geometry of five-dimensional Kerr black holes is discussed based on geodesics and Weyl curvatures. Kerr-Star space, Star-Kerr space and Kruskal space are naturally introduced by using special null geodesics. We show that the geodesics of AdS Kerr black hole are integrable, which generalizes the result of Frolov and Stojkovic. We also show that five-dimensional AdS Kerr black holes are isospectrum deformations of Ricci-flat Kerr black holes in the sense that the eigenvalues of the Weyl curvature are preserved.