Higher dimensional Kerr-Schild spacetimes
arXiv:0808.2165 · doi:10.1088/0264-9381/26/2/025008
Abstract
We investigate general properties of Kerr-Schild (KS) metrics in n>4 spacetime dimensions. First, we show that the Weyl tensor is of type II or more special if the null KS vector k is geodetic (or, equivalently, if T_{ab}k^ak^b=0). We subsequently specialize to vacuum KS solutions, which naturally split into two families of non-expanding and expanding metrics. After demonstrating that non-expanding solutions are equivalent to the known class of vacuum Kundt solutions of type N, we analyze expanding solutions in detail. We show that they can only be of the type II or D, and we characterize optical properties of the multiple Weyl aligned null direction (WAND) k. In general, k has caustics corresponding to curvature singularities. In addition, it is generically shearing. Nevertheless, we arrive at a possible "weak" n>4 extension of the Goldberg-Sachs theorem, limited to the KS class, which matches previous conclusions for general type III/N solutions. In passing, properties of Myers-Perry black holes and black rings related to our results are also briefly discussed.
33 pages. v2: minor changes, new references
References in corpus (19)
- A rotating black ring in five dimensions
- Rotation and the AdS/CFT correspondence
- The General Kerr-de Sitter Metrics in All Dimensions
- Classification of the Weyl Tensor in Higher Dimensions
- General Kerr-NUT-AdS Metrics in All Dimensions
- Particle and light motion in a space-time of a five-dimensional rotating black hole
- Alignment and algebraically special tensors in Lorentzian geometry
- Vanishing Scalar Invariant Spacetimes in Higher Dimensions
- Robinson-Trautman spacetimes in higher dimensions
- Bianchi identities in higher dimensions
- Type D Einstein spacetimes in higher dimensions
- Ricci identities in higher dimensions
- Higher dimensional VSI spacetimes
- Generalizations of pp-wave spacetimes in higher dimensions
- Kerr-NUT-de Sitter Curvature in All Dimensions
- WANDs of the Black Ring
- Killing-Yano tensors and multi-hermitian structures
- Newman-Penrose formalism in higher dimensions: vacuum spacetimes with a non-twisting geodetic multiple Weyl aligned null direction
- Higher dimensional spacetimes with a geodesic, shearfree, twistfree and expanding null congruence
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- Newman-Penrose formalism in higher dimensions: vacuum spacetimes with a non-twisting geodetic multiple Weyl aligned null direction
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- Approach of background metric expansion to a new metric ansatz for gauged and ungauged Kaluza-Klein supergravity black holes
- On the Six-dimensional Kerr Theorem and Twistor Equation
- On the uniqueness of the Kerr-(A)dS metric as a type II(D) solution in six dimensions
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