Type D Einstein spacetimes in higher dimensions
| dc.creator | Pravda, Vojtech | |
| dc.creator | Pravdova, Alena | |
| dc.creator | Ortaggio, Marcello | |
| dc.date | 2007-04-03 | |
| dc.date | 2007-07-22 | |
| dc.date.accessioned | 2026-07-07T11:20:08Z | |
| dc.date.available | 2026-07-07T11:20:08Z | |
| dc.description | We show that all static spacetimes in higher dimensions are of Weyl types G, I_i, D or O. This applies also to stationary spacetimes if 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.) Next we demonstrate that the same Weyl types characterize warped product spacetimes with a one-dimensional Lorentzian (timelike) factor, whereas warped spacetimes with a two-dimensional Lorentzian factor are restricted to the types D or O. By exploring the Bianchi identities, we then analyze the simplest non-trivial case from the above classes - type D vacuum spacetimes, possibly with a cosmological constant, dropping, however, the assumptions that the spacetime is static, stationary or warped. It is shown that for ``generic'' type D vacuum spacetimes the corresponding principal null directions are geodetic in any dimension (this applies also to type II spacetimes). For n>=5, however, there may exist particular cases of type D spacetimes which admit non-geodetic multiple principal null directions and we present such examples in any n>=7. Further studies are restricted to five dimensions, where the type D Weyl tensor is described by a 3x3 matrix Φ_{ij}. In the case with ``twistfree'' (A_{ij}=0) principal null geodesics we show that in a ``generic'' case Φ_{ij} is symmetric and eigenvectors of Φ_{ij} coincide with those of the expansion matrix S_{ij}, providing us with three preferred spacelike directions of the spacetime. Similar results are also obtained when relaxing the twistfree condition and assuming instead that Φ_{ij} is symmetric. The n=5 Myers-Perry black hole and Kerr-NUT-AdS metrics in arbitrary dimension are briefly studied as specific examples of type D vacuum spacetime. | |
| dc.description | 24 pages. v2: new appendix on geometric optics of higher dimensional Kerr-NUT-AdS black holes, minor changes in the text. To appear in Class.Quant.Grav | |
| dc.identifier | https://arxiv.org/abs/0704.0435 | |
| dc.identifier | http://arxiv.org/abs/0704.0435 | |
| dc.identifier | Class.Quant.Grav.24:4407-4428,2007 | |
| dc.identifier | doi:10.1088/0264-9381/24/17/009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/193870 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Type D Einstein spacetimes in higher dimensions | |
| dc.type | text |