Algebraic classification of higher dimensional spacetimes based on null alignment

Understand

We review recent developments and applications of the classification of the Weyl tensor in higher dimensional Lorentzian geometries.

• First, we discuss the general setup, i.e.
• main definitions and methods for the classification, some refinements and the generalized Newman-Penrose and Geroch-Held-Penrose formalisms.
• Next, we summarize general results, such as a partial extension of the Goldberg-Sachs theorem, characterization of spacetimes with vanishing (or constant) curvature invariants and the peeling behaviour in asymptotically flat spacetimes.