Generating rotating black hole solutions by using the Cayley-Dickson construction

TL;DR

This paper introduces a novel method using Cayley-Dickson algebra to efficiently generate higher-dimensional rotating black hole solutions, including the nine-dimensional Myers-Perry black hole with multiple angular momenta.

Contribution

It develops a new approach combining Cayley-Dickson algebra with the Janis-Newman algorithm to produce rotating black hole solutions across various dimensions.

Findings

Derived the nine-dimensional Myers-Perry solution with four angular momenta.

Established a formula linking Cayley-Dickson algebra dimension to maximum angular momenta.

Discussed the limitations and cutoff for using Cayley-Dickson construction in this context.

Abstract

This paper exploits the power of the Cayley-Dickson algebra to generate stationary rotating black hole solutions in one fell swoop. Specifically, we derive the nine-dimensional Myers-Perry solution with four independent angular momenta by using the Janis-Newman algorithm and Giampieri's simplification method, exploiting the octonion algebra. A general formula relating the dimension of the Cayley-Dickson algebra with the maximum number of angular momenta in each dimension is derived. Finally, we discuss the cut-off dimension for using the Cayley-Dickson construction along with the Janis-Newman algorithm for producing the rotating solutions.