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

TL;DR

This paper proves that under certain conditions, six-dimensional vacuum spacetimes with specific Weyl properties are uniquely classified as generalized Myers-Perry black hole solutions, including limits and special cases.

Contribution

It establishes a classification theorem showing such spacetimes are Kerr-Schild type D solutions, specifically generalized Myers-Perry metrics, under asymptotic fall-off assumptions.

Findings

All solutions are Kerr-Schild type D spacetimes.

Solutions include generalized Myers-Perry metrics and their limits.

Special cases include twisting solutions with zero shear.

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.