Generating rotating black hole solutions by using the Cayley-Dickson construction
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.
Cite
@article{arxiv.2212.09882,
title = {Generating rotating black hole solutions by using the Cayley-Dickson construction},
author = {Zahra Mirzaiyan and Giampiero Esposito},
journal= {arXiv preprint arXiv:2212.09882},
year = {2023}
}
Comments
27 pages, Latex. In the final version, the presentation has been improved, misprints no longer occur, and 3 references have been added