Petrov types of slowly rotating fluid balls

Details Petrov types of slowly rotating fluid balls Petrov types of slowly rotating fluid balls

1999-11-18

arxiv.org/abs/gr-qc/9911068v2

Gen.Rel.Grav. 32 (2000) 2319-2332

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, version to appear in Gen. Rel. Grav

Scientific paper

Circularly rotating axisymmetric perfect fluid space-times are investigated to second order in the small angular velocity. The conditions of various special Petrov types are solved in a comoving tetrad formalism. A number of theorems are stated on the possible Petrov types of various fluid models. It is shown that Petrov type II solutions must reduce to the de Sitter spacetime in the static limit. Two space-times with a physically satisfactory energy-momentum tensor are investigated in detail. For the rotating incompressible fluid, it is proven that the Petrov type cannot be D. The equation of the rotation function $\omega $ can be solved for the Tolman type IV fluid in terms of quadratures. It is also shown that the rotating version of the Tolman IV space-time cannot be Petrov type D.

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