Shear-free homogeneous cosmological model with heat flux

Abstract

We present the condition of vanishing shear in a spatially homogeneous spacetime in terms of the Ricci rotation co-efficients corresponding to an orthonormal tetrad (ν α. A η α) (whereν α is the unit vector along the time axis and A η α are the three independent reciprocal group vectors). Assuming that the velocity vector can be expanded in the direction ofν α and any one of the A η α’s it is shown that shear-free motion is possible only in case of some special Bianchi types, and these cases are studied assuming the velocity vector to be geodetic and that there may be a nonvanishing heat flux term.