Kerr-NUT-de Sitter Curvature in All Dimensions

TL;DR

This paper explicitly computes the Riemannian curvature of Kerr-NUT-de Sitter metrics in all dimensions, clarifies the Einstein condition for these metrics, and classifies their algebraic type.

Contribution

It provides a unified, concise expression for the curvature of Kerr-NUT-de Sitter metrics across all dimensions and clarifies their Einstein condition and algebraic classification.

Findings

Curvature expressed using a single function

Einstein condition for these metrics is clarified

Metrics are classified as type D

Abstract

We explicitly calculate the Riemannian curvature of D-dimensional metrics recently discussed by Chen, Lu and Pope. We find that they can be concisely written by using a single function. The Einstein condition which corresponds to the Kerr-NUT-de Sitter metric is clarified for all dimensions. It is shown that the metrics are of type D.