Exact power law metrics in cosmology

Spatially homogeneous and non-exceptional spatially self-similar spacetime metrics which are 'exact power law metrics' are defined, explicitly parametrised and shown to have fixed conformal 3-geometry in the natural slicing of the spacetime by the orbits of the symmetry group and to admit a homothetic Killing vector field not tangent to that slicing. In fact the exact power metrics are exactly those spatially homogeneous and spatially self-similar metrics which admit a homothetic Killing vector field not tangent to the spacelike orbits of the homogeneity or self-similarity group. Such metrics arise as 'singular point solutions' of gravitational field equations when formulated as a certain system of first order differential equations. These special exact solutions play an important role in the qualitative behaviour of the general solution of a given set of field equations and sources with these symmetries.