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

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.