Twistor Construction of Higher-Dimensional Black Holes - Part II: Examples

TL;DR

This paper demonstrates how to construct higher-dimensional black hole solutions using twistor methods, applying the approach to known five-dimensional examples and proposing a new ansatz based on rod structures and angular momenta.

Contribution

It introduces a new ansatz for deriving patching matrices from rod structures and angular momenta, validated on several five-dimensional black hole solutions.

Findings

Successfully reconstructs known solutions like flat space, Myers-Perry black holes, and black rings.

Develops rules for patching matrix transitions and conical singularity elimination.

Validates the ansatz on examples with up to three nuts.

Abstract

We apply the twistor construction for higher-dimensional black holes to known examples in five space-time dimensions. First the patching matrices are calculated from the explicit metric for these examples. Then an ansatz is proposed for obtaining the patching matrix instead from the data of rod structure and angular momenta. The ansatz is tested on examples with up to three nuts, and these are shown to give flat space, the Myers-Perry solution and the black ring, as expected. Rules for the transition between different adaptations of the patching matrix and for the elimination of conical singularities are developed and seen to work.