Classification of Robinson-Trautmann and Kundt Geometries with Large D Limit

Algebraic classification of higher dimensional, shear-free, twist-free, expanding (or non-expanding) spacetime is studied with the limit of $D\rightarrow\infty$. 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 $D\rightarrow \infty$, the components of Weyl scalar are obtained much simpler. Without solving field equations, by determining obligotary 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 $I_{i}$, Type $II_{i}$, Type $III_{i}$ and Type D(a-b-c-d) for secondary WAND.