Shear-free perfect fluids with a solenoidal electric curvature

We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of the Weyl tensor is zero.

Purely magnetic locally rotationally symmetric spacetimes

We consider all purely magnetic, locally rotationally symmetric (LRS) spacetimes. It is shown that such spacetimes belong to either LRS class I or III by the Ellis classification. For each class the most general solution is found exhibiting a disposable function and three parameters. A Segré classification of purely magnetic LRS spacetimes is given together with the compatibility requirements of two general energy–momentum tensors. Finally, implicit solutions are obtained, in each class, when the energy–momentum tensor is a perfect fluid.