Five-dimensional Janis-Newman algorithm

TL;DR

This paper extends the Janis-Newman algorithm to five dimensions with two angular momenta, providing a unified framework for generating stationary solutions in higher-dimensional gravity, exemplified by Myers-Perry and BMPV black holes.

Contribution

It introduces a novel extension of the Janis-Newman algorithm to five dimensions with two angular momenta, broadening its applicability to higher-dimensional black hole solutions.

Findings

Successfully applied to Myers-Perry and BMPV black holes

Proposes potential generalizations to higher dimensions and angular momenta

Highlights challenges in dimensions higher than six

Abstract

The Janis-Newman algorithm has been shown to be successful in finding new sta- tionary solutions of four-dimensional gravity. Attempts for a generalization to higher dimensions have already been found for the restricted cases with only one angular mo- mentum. In this paper we propose an extension of this algorithm to five dimensions with two angular momenta - using the prescription of G. Giampieri - through two specific examples, that are the Myers-Perry and BMPV black holes. We also discuss possible enlargements of our prescriptions to other dimensions and maximal number of angular momenta, and show how dimensions higher than six appear to be much more challenging to treat within this framework. Nonetheless this general algorithm provides a unification of the formulation in d = 3, 4, 5 of the Janis-Newman algorithm, from which which expose several examples including the BTZ black hole.