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

Abstract

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 $U^0=\pm 1/2,0$. 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.

30 pages. v2: a few typos fixed, added references, minor improvements (results unchanged)

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Cited by in corpus (7)

• Charging Kerr-Schild spacetimes in higher dimensions
• Classification of Kerr-de Sitter-like spacetimes with conformally flat $\mathcal{I}$ in all dimensions
• On higher dimensional Einstein spacetimes with a non-degenerate double Weyl aligned null direction
• On the uniqueness of the Kerr-(A)dS metric as a type II(D) solution in six dimensions
• Einstein manifolds with optical geometries of Kerr type
• On type II(D) Einstein spacetimes in six dimensions
• Higher-dimensional black holes with multiple equal rotations