Petrov classification of a non-static axially symmetric torodial distribution

A non-static axially symmetric torodial space time has been considered. The Petrov classification gives rise to nine distinct cases. The Segre characteristics in these cases have studied. It has been found that the metric belongs to type I, Isub(D) or type II under certain conditions. It is shown that the metric does not admit empty space-time. It is also found that gravitational collapse with escaping neutrinos is not permissible in this case. (author)