Classification of Robinson-Trautman and Kundt geometries with Large D limit

Abstract

Algebraic classification of higher dimensional, shear-free, twist-free, expanding (or non-expanding) spacetime is studied with the limit of D → ∞. Similar to classification of any arbitrary dimension D > 4, this spacetime is Type I(b) or more special, according to our calculations. However, thanks to the method of taking the limit of dimension D → ∞, the relevant Weyl scalars become much simpler. Without solving field equations, by determining obligatory conditions to the components of Weyl scalar vanish, the spacetime is classified Type I(a), Type II(a-b-c-d), Type III(a-b), Type N and Type O for primary Weyl aligned null direciton (WAND), and Type Ii, Type IIi, Type IIIi and Type D(a-b-c-d) for secondary WAND.