One can consider a perfect fluid as the fermionic component such that the stress-energy tensor takes the standard form for more about fluids in relativity). In most work with fermionic-boson stars, the fluid is described by a degenerate, relativistic Fermi gas, so that the pressure is given by the parametric equation of state of Chandrasekhar
The perfect fluid obeys relativistic versions of the Euler equations, which account for the conservation of the fluid energy and momentum, plus the conservation of the baryonic number (i.e., mass conservation). The complex scalar field representing the bosonic component is once again described by the Klein–Gordon equation. The spacetime is computed through the Einstein equations with a stress-energy tensor, which is a combination of the complex scalar field and the perfect fluid
These equations can be written in adimensional form by rescaling the variables by introducing the following quantities
It was shown that the stability arguments made with boson stars can also be applied to these mixed objects . The existence of slowly rotating fermion-boson stars was shown in , although no solutions were found in previous attempts . Also see  for unstable solutions consisting of a real scalar field coupled to a perfect fluid with a polytropic equation of state.
Living Rev. Relativity 15, (2012), 6
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