Interaction of fluids described through relative motion and application to Bianchi type-I spacetimes

Abstract: We derive the stress-energy tensor for a pair of fluids with a novel form of interaction that depends on the relative velocity of volume elements of the two fluids. The interaction is described through quantities measuring the local particle density of one fluid through the metric tensor induced on hypersurfaces perpendicular to the 4-velocity field of the other fluid -- the particle density of one fluid measured in reference frames of volume elements of the other fluid, as opposed to the standardly defined particle density of a fluid measured in reference frames of its own volume elements. This introduces an explicit dependence of the stress-energy tensor on the scalar product of 4-velocities of the two fluids, which can be expressed through the relative physical speed of their volume elements. We also investigate the effect of the studied interaction on the evolution of Bianchi type-I spacetimes, under the assumption of small anisotropy. This represents the simplest nontrivial application of the studied form of interaction. The evolution of the anisotropy does not change qualitatively, which implies compatibility with models of our Universe.