Five-dimensional metrics of Petrov type 22

TL;DR

This paper classifies five-dimensional Einstein manifolds with specific symmetry and Petrov type, and applies this to show that localized black holes in a certain model must have Petrov type 4.

Contribution

It provides a complete classification of certain five-dimensional Einstein manifolds and applies this to black hole Petrov type determination in the Randall-Sundrum model.

Findings

All five-dimensional Einstein manifolds with the specified properties are classified.

Localized black holes in the Randall-Sundrum scenario necessarily have Petrov type 4.

Abstract

We classify all five-dimensional Einstein manifolds that are static, have an SO(3) isometry group and have Petrov type 22. We use this classification to show that the localized black hole in the Randall-Sundrum scenario necessarily has Petrov type 4.