MG11 
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Classification results on purely magnetic perfect fluid models

\emph{Abstract.} A non-conformally flat perfect fluid model for which the electric part of the Weyl tensor w.r.t.\ the fluid 4-velocity field vanishes, is called a \emph{purely magnetic perfect fluid} (PMpf). Most recently, we showed that PMpf's of Petrov type D are necessarily locally rotationally symmetric, and hence are all known. Secondly, the class of algebraically general, non-accelerating PMpf's was explored. The irrotational subclass turns out to contain a physically plausible and essentially unique member. Thirdly, the case of constant pressure is probably inconsistent because of a striking mathematical feature in the governing equations. These three topics are presented, in each case revealing the strength of the used formalism (NP/GHP, orthonormal tetrad and 1+3 covariant technique, respectively).

Classification results on purely magnetic perfect fluid models

A non-conformally flat perfect fluid model for which the electric part of the Weyl tensor w.r.t.\ the fluid 4-velocity field vanishes, is called a \emph{purely magnetic perfect fluid} (PMpf). Most recently, we showed that PMpf's of Petrov type D are necessarily locally rotationally symmetric, and hence are all known. Secondly, the class of algebraically general, non-accelerating PMpf's was explored. The irrotational subclass turns out to contain a physically plausible and essentially unique member. Thirdly, the case of constant pressure is probably inconsistent because of a striking mathematical feature in the governing equations. These three topics are presented, in each case revealing the strength of the used formalism (NP/GHP, orthonormal tetrad and 1+3 covariant technique, respectively).

Purely electric perfect fluids of Petrov type D

Purely electric perfect fluids (PEpf's) are characterized by the vanishing of the magnetic part of the Weyl tensor w.r.t. the fluid congruence. Many important examples of such models exist. Based on the Bianchi identities PEpf's are naturally divided into three subclasses. The first subclass only possesses non-rotating members and is shown to be partitioned into the LRS class II, the shearfree and the Szekeres dust models, all fully known. It is found that any member of the second subclass must have an equation of state \mu=p+c and a vorticity vector lying in the plane of the repeated principal null directions. Further results from this classification analysis will be discussed. This is most recent work, inspired by and completing previous investigations by Carminati, Wainwright, Barnes, Rowlingson and Collins.