Two-fluid Schwarzschild solution

We consider the interior two-fluid Schwarzschild solution. That is a model of compact (neutron) stars with admixed dark matter. The two constant energy densities generalize the interior Schwarschild solution to the case of two fluids (representing standard model matter and dark matter, for instance), interacting mutually solely by the common gravitational field. In general, the two-fluid core is surrounded by a one-fluid corona (envelope). Only for special parameters (the model depends on energy densities e₁,e₂ e 1 , e 2 and central pressures pc1,pc2 p c 1 , p c 2 of the fluids), both fluids occupy the same region. Despite the sum of two energy densities in that region, the compactness bound of 4/9 is not exceeded. Therefore, a Buchdahl limit for two fluids holds. A conceivable object is one with a stark leakage of one fluid (e.g. dark matter) beyond the two-fluid core.