  When solving the equations of General Relativity in a symmetric sector, it is
natural to consider the same symmetry for the geometry and stress-energy. This
implies that for static and isotropic spacetimes, the most general natural
stress-energy tensor is a sum of a perfect fluid and a radial imperfect fluid
component. In the special situations where the perfect fluid component vanishes
or is a spacetime constant, the solutions to Einstein's equations can be
thought of as modified Schwarzschild and Schwarzschild-de Sitter spaces. Exact
solutions of this type are derived and it is shown that whereas deviations from
the unmodified solutions can be made small, among the manifestations of the
imperfect fluid component is a shift in angular momentum scaling for orbiting
test-bodies at large radius. Based on this effect, the question of whether the
imperfect fluid component can feasibly describe dark matter phenomenology is
addressed.
