Classification of Robinson-Trautmann 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 $D\to \infty$. 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 $D\to \infty$, 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 $I{I}_i$, Type $II{I}_i$ and Type D(a-b-c-d) for secondary WAND.

17 pages, comments are welcome

References in corpus (7)

• Robinson-Trautman spacetimes in higher dimensions
• General Kundt spacetimes in higher dimensions
• Robinson-Trautman spacetimes with an electromagnetic field in higher dimensions
• Static and radiating p-form black holes in the higher dimensional Robinson-Trautman class
• Algebraic structure of Robinson-Trautman and Kundt geometries in arbitrary dimension
• Lattice Black Branes at Large $D$
• Squashed black holes at large $D$

Cited by in corpus (2)

• The Newman-Penrose formalism in quadratic gravity
• Analyzes of Algebraic Classification of Higher Dimensional Kundt Geometries with Large $D$ Method