On the uniqueness of the Myers-Perry spacetime as a type II(D) solution in six dimensions

• Published in: The journal of high energy physics Vol. 2017; no. 6; pp. 1 - 40
• Main Author: Ortaggio, Marcello
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2017; Springer Nature B.V; SpringerOpen
• Subjects: Alignment; Asymptotic properties; Black Holes; Classical and Quantum Gravitation; Classical Theories of Gravity; Eigenvalues; Elementary Particles; High energy physics; Mathematical analysis; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Shear; Spacetime; String Theory; Twisting; Uniqueness; Classical Theories of Gravity; Black Holes
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2017)042

A bstract We study the class of vacuum (Ricci flat) six-dimensional spacetimes admitting a non-degenerate multiple Weyl aligned null direction ℓ , thus being of Weyl type II or more special. Subject to an additional assumption on the asymptotic fall-off of the Weyl tensor, we prove that these spacetimes can be completely classified in terms of the two eigenvalues of the (asymptotic) twist matrix of ℓ and of a discrete parameter U 0 = ±1 / 2 , 0. All solutions turn out to be Kerr-Schild spacetimes of type D and reduce to a family of “generalized” Myers-Perry metrics (which include limits and analytic continuations of the original Myers-Perry black hole metric, such as certain NUT spacetimes). A special subcase corresponds to twisting solutions with zero shear. In passing, limits connecting various branches of solutions are briefly discussed.