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 simplif...

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Bibliographic Details
Published inarXiv.org
Main Authors Mirzaiyan, Zahra, Esposito, Giampiero
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.01.2023
Subjects
Algebra
Algorithms
Physics - General Relativity and Quantum Cosmology
Physics - High Energy Physics - Theory
Rotation
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2212.09882