Generating rotating black hole solutions by using the Cayley-Dickson construction
arXiv:2212.09882 · doi:10.1016/j.aop.2023.169223
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.
arXiv comment27 pages, Latex. In the final version, the presentation has been improved, misprints no longer occur, and 3 references have been added
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