Static spherically symmetric stiff matter in general relativity

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.