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Einstein's field equations for the case of a static and spherically symmetric distribution of stiff matter are considered. The problem is reduced to a single second-order non-linear differential equation for which a class of three particular solutions is obtained. Two of the solutions correspond to flat spacetime and the Schwarzschild metric respectively. The third solution leads to a new metric, the first of its kind, which takes a very simple form in canonical coordinates. The pressure (and energy density) vanish at spatial infinity and diverge at the centre, and thus the solution could represent a cosmological model with a central singularity.

We propose a new method to build exact solutions of Einstein field equations in case of ‘‘hypersurface-homogeneous space-times.’’ The energy-momentum tensor is of perfect fluid type. Starting from SE solutions we are able to build new classes of solutions which add to the rare solutions not satisfying the equation of state p=(γ−1)μ. We study the geometrical and physical properties of some of the solutions obtained.

A method for generating exact Bianchi type II cosmological models with a perfect fluid distribution of matter is presented. Two new classes of Bianchi type II solutions have been generated from Lorenz’s solution [D. Lorenz, Phys. Lett. A 79, 19 (1980)]. A detailed study of physical and kinematic properties of one of them has been carried out.

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