A Petrov type I and generically asymmetric rotating dust family

TL;DR

This paper constructs a family of algebraically general rotating dust models with specific properties, revealing new Petrov type I space-times that require advanced classification techniques.

Contribution

It introduces a new family of rotating dust solutions with unique algebraic and geometric properties, including asymmetric solutions with constant energy density and vorticity ratio.

Findings

First examples of Petrov type I space-times requiring third covariant derivative for classification

Construction of a family of algebraically general, gravito-electric, expanding, rotating dust models

Identification of solutions with constant energy density and vorticity ratio

Abstract

The general line element corresponding to the family of algebraically general, gravito-electric, expanding, rotating dust models with one functionally independent zero-order Riemann invariant is constructed. The isometry group is at most one-dimensional but generically trivial. It is shown that the asymmetric solutions with constant ratio of energy density and vorticity amplitude provide first examples of Petrov type I space-times for which the Karlhede classification requires the computation of the third covariant derivative of the Riemann tensor.