On type II(D) Einstein spacetimes in six dimensions

Abstract

After a concise overview of Einstein spacetimes of type II (or more special) in four and five dimensions, we summarize recent results in the six-dimensional case. We assume the optical matrix to be non-degenerate and ``generic'', and the Weyl tensor to fall off sufficiently rapidly at infinity. As it turns out, the most general metric is characterized by one discrete (normalized) and three continuous parameters, is of type D and belongs to the Kerr-Schild class. Its relation to the previously known Kerr-(A)dS and Kerr-NUT-(A)dS metrics is clarified.

6 pages; short summary of 2505.10532 [gr-qc]. Proceedings of "60 Years in Mathematical Physics: Honoring Prof. Metin Gürses", Ankara, December 26th, 2025 (https://sites.google.com/view/gurses2025)

References in corpus (29)

• The General Kerr-de Sitter Metrics in All Dimensions
• Black holes and the double copy
• Classification of the Weyl Tensor in Higher Dimensions
• General Kerr-NUT-AdS Metrics in All Dimensions
• The Kerr-Schild double copy in curved spacetime
• Robinson-Trautman spacetimes in higher dimensions
• Bianchi identities in higher dimensions
• Type D Einstein spacetimes in higher dimensions
• Ricci identities in higher dimensions
• Kerr-NUT-de Sitter Curvature in All Dimensions
• Nuttier (A)dS Black Holes in Higher Dimensions
• Kerr-Schild spacetimes with (A)dS background
• Gyromagnetic Ratio of Charged Kerr-Anti-de Sitter Black Holes
• Peeling of the Weyl tensor and gravitational radiation in higher dimensions
• Kerr-Schild Structure and Harmonic 2-forms on (A)dS-Kerr-NUT Metrics
• On a five-dimensional version of the Goldberg-Sachs theorem
• Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation
• Classification of Higher Dimensional Spacetimes
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Type III and N Einstein spacetimes in higher dimensions: general properties
• On asymptotically flat algebraically special spacetimes in higher dimensions
• On higher dimensional Einstein spacetimes with a warped extra dimension
• Weakly charged generalized Kerr-NUT-(A)dS spacetimes
• On algebraically special vacuum spacetimes in five dimensions
• Twisting algebraically special solutions in five dimensions
• Classification of Kerr-de Sitter-like spacetimes with conformally flat $\mathcal{I}$ in all dimensions
• Twisting non-shearing congruences of null geodesics, almost CR structures, and Einstein metrics in even dimensions
• On the uniqueness of the Myers-Perry spacetime as a type II(D) solution in six dimensions
• On the uniqueness of the Kerr-(A)dS metric as a type II(D) solution in six dimensions