Partially locally rotationally symmetric perfect fluid cosmologies

Details Partially locally rotationally symmetric perfect fluid cosmologies Partially locally rotationally symmetric perfect fluid cosmologies

1999-12-27

arxiv.org/abs/gr-qc/9912107v2

Class.Quant.Grav. 17 (2000) 3135-3156

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, LaTeX2.09 (10pt), no figures; shortened revised version, new references; accepted for publication in Classical and Q

Scientific paper

10.1088/0264-9381/17/16/304

We show that there are no new consistent cosmological perfect fluid solutions when in an open neighbourhood ${\cal U}$ of an event the fluid kinematical variables and the electric and magnetic Weyl curvature are all assumed rotationally symmetric about a common spatial axis, specialising the Weyl curvature tensor to algebraic Petrov type D. The consistent solutions of this kind are either locally rotationally symmetric, or are subcases of the Szekeres dust models. Parts of our results require the assumption of a barotropic equation of state. Additionally we demonstrate that local rotational symmetry of perfect fluid cosmologies follows from rotational symmetry of the Riemann curvature tensor and of its covariant derivatives only up to second order, thus strengthening a previous result.

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