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We prove that higher dimensional Einstein spacetimes which possess a geodesic, non-degenerate double Weyl aligned null direction (WAND) $ell$ must additionally possess a second double WAND (thus being of type D) if either: (a) the Weyl tensor obeys $C_{abc[d}ell_{e]}ell^c=0$ ($LeftrightarrowPhi_{ij}=0$, i.e., the Weyl type is II(abd)); (b) $ell$ is twistfree. Some comments about an extension of the Goldberg-Sachs theorem to six dimensions are also made.
We prove that any asymptotically flat static spacetime in higher dimensional Einstein-Maxwell theory must have no magnetic field. This implies that there are no static soliton spacetimes and completes the classification of static non-extremal black h
We present the explicit metric forms for higher dimensional vanishing scalar invariant (VSI) Lorentzian spacetimes. We note that all of the VSI spacetimes belong to the higher dimensional Kundt class. We determine all of the VSI spacetimes which admi
In this paper we investigate whether the holographic principle proposed in string theory has a classical counterpart in general relativity theory. We show that there is a partial correspondence: at least in the case of vacuum Petrov type D spacetimes
We algebraically classify some higher dimensional spacetimes, including a number of vacuum solutions of the Einstein field equations which can represent higher dimensional black holes. We discuss some consequences of this work.
Gravitational waves are one of the most important diagnostic tools in the analysis of strong-gravity dynamics and have been turned into an observational channel with LIGOs detection of GW150914. Aside from their importance in astrophysics, black hole