2006/04/30 by W. Chen, W Chen, H. Lü +3 · 21 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Computer science #Diagonal #Dimension (graph theory) #General relativity #Generalization #Geometry #Homogeneous space #Kerr metric #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Nonlinear Waves and Solitons #Nut #Physics #Pure mathematics #RADIUS #Rotation (mathematics) #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/23/17/013
published as Class.Quant.Grav.23:5323-5340,2006 · Latex, 24 pages, minor typos corrected
arxiv created 2006/05/23 · openalex publication_date 2006/08/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Kerr–AdS metric in dimension D has cohomogeneity [ D /2]; the metric components depend on the radial coordinate r and [ D /2] latitude variables μ i that are subject to the constraint ∑ i μ 2 i = 1. We find a coordinate reparametrization in which the μ i variables are replaced by [ D /2] − 1 unconstrained coordinates y α , and having the remarkable property that the Kerr–AdS metric becomes diagonal in the coordinate differentials d y α . The coordinates r and y α now appear in a very symmetrical way in the metric, leading to an immediate generalization in which we can introduce [ D /2] − 1 NUT parameters. We find that ( D − 5)/2 are non-trivial in odd dimensions whilst ( D − 2)/2 are non-trivial in even dimensions. This gives the most general Kerr–NUT–AdS metric in D dimensions. We find that in all dimensions D ⩾ 4, there exist discrete symmetries that involve inverting a rotation parameter through the AdS radius. These symmetries imply that Kerr–NUT–AdS metrics with over-rotating parameters are equivalent to under-rotating metrics. We also consider the BPS limit of the Kerr–NUT–AdS metrics, and thereby obtain, in odd dimensions and after Euclideanization, new families of Einstein–Sasaki metrics.