Static and stationary dark fluid universes: A gravitoelectromagnetic perspective

We introduce a physical characterization of the static and stationary perfect fluid solutions of the Einstein field equations with a single or 2-component perfect fluid sources, according to their gravitoelectric and gravitomagnetic fields. The absence or presence of either or both of these fields could restrict the equations of state of the underlying perfect fluid sources. As the representative of each family of solutions, we consider those spaces that include the cosmological term as a dark fluid source with the equation of state $p=-\rho = constant$.