Petrov types of slowly rotating fluid balls (Q5930585)

Petrov types of slowly rotating fluid balls are studied. In Part 2 Theorem 1 is given: ``Circularly and rigidly rotating perfect fluids of Petrov type II must reduce to the de Sitter space-time in the slow-rotation limit''. In Part 3 Theorem 2 is given: ``A slowly and circularly rotating incompressible perfect fluid space-time with an asymptotically vacuum exterior cannot be Petrov type D''. In Part 4 the interesting Theorem 3 is given: ``A rotating perfect fluid space-time that reduces to the Tolman IV solution in the static limit and can be matched to an asymptotically flat vacuum exterior cannot be Petrov type D'' [see \textit{R. Tolman}, Phys. Rev. (2) 55, 364-373 (1939; Zbl 0020.28407)]. Explicit expressions are obtained for the coefficients of these equations.