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. •This paper derives, for the first time in the literature, the nine-dimensional Myers–Perry solution by using the Janis-Newman algorithm.