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

TL;DR

This paper classifies higher-dimensional Robinson-Trautmann and Kundt spacetimes in the large D limit, simplifying the Weyl scalar components and identifying algebraic types without solving field equations.

Contribution

It introduces a novel large D limit approach to classify these spacetimes algebraically, simplifying calculations and providing a comprehensive classification scheme.

Findings

Weyl scalar components become simpler in the large D limit.

Spacetimes are classified into various algebraic types without solving field equations.

The method applies to both shear-free, twist-free, expanding and non-expanding cases.

Abstract

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.