Type D Einstein spacetimes in higher dimensions

@article{Pravda2007TypeDE,
  title={Type D Einstein spacetimes in higher dimensions},
  author={Vojtěch Pravda and Alena Pravdov{\'a} and Marcello Ortaggio},
  journal={Classical and Quantum Gravity},
  year={2007},
  volume={24},
  pages={4407 - 4428}
}
We show that all static spacetimes in higher dimensions n > 4 are necessarily of Weyl types G, Ii, D or O. This also applies to stationary spacetimes provided additional conditions are fulfilled, as for most known black hole/ring solutions. (The conclusions change when the Killing generator becomes null, such as at Killing horizons, on which we briefly comment.) Next we demonstrate that the same Weyl types characterize warped product spacetimes with a one-dimensional Lorentzian (timelike… 

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