Algebraically general, gravito-electric rotating dust

TL;DR

This paper investigates a specific class of rotating dust space-times in general relativity, focusing on their invariant properties, limits, and special subclasses, including connections to known solutions like the G"odel universe.

Contribution

It characterizes the invariant properties of algebraically general, gravito-electric rotating dust solutions and explores their limits and special subclasses, including irrotational and shear-free cases.

Findings

Number of independent invariants is 1 or 2.

Limit for vanishing vorticity connects to irrotational dust solutions.

Shear-free limit corresponds to the G"odel universe.

Abstract

The class of gravito-electric, algebraically general, rotating `silent' dust space-times is studied. The main invariant properties are deduced. The number $t_0$ of functionally independent zero-order Riemann invariants satisfies $1\leq t_0\leq 2$ and special attention is given to the subclass $t_0=1$. Whereas there are no $\Lambda$-term limits comprised in the class, the limit for vanishing vorticity leads to two previously derived irrotational dust families with $\Lambda>0$, and the shear-free limit is the G\"{o}del universe.