A Petrov type I and generically asymmetric rotating dust family

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.

7 pages, irrotational limit case added, several minor errors corrected

References in corpus (2)

• Silent universes with a cosmological constant
• The type N Karlhede bound is sharp

Cited by in corpus (4)

• Minimal tensors and purely electric or magnetic spacetimes of arbitrary dimension
• Three-dimensional spacetimes of maximal order
• Gravitomagnetism and the significance of the curvature scalar invariants
• Poynting vector, super-Poynting vector, and principal observers in electromagnetism and general relativity