Generalized similarity solutions for the type D fluid in five-dimensional flat space

The partial differential equation corresponding to the metric function in a five-dimensional flat space describing the perfect fluid distribution has been examined for generalized symmetries via a new approach. It is shown that the approach utilized here has, besides providing generalized symmetries, for some particular values of the parameters involved, yielded new metrics and Petrov type D solutions. Further, for the general case the problem is reduced to the solution of an Abel’s equation of second kind, which obviously generalizes the scope for new metrics and new Petrov type D solutions.