TOV equations form of anisotropic pressure on two fluid models

Abstract

We construct Tolman Oppenheimer Volkoff (TOV) equations for anisotropic pressure of two non-interacted perfect fluid with different four-velocities. This paper’s primary motivation is that we obtain the result that could describe the neutron stars (NS) admixed with dark matter (DM) that satisfying constraint from GW190814. Otherwise, our result also can investigate other compact objects that are admixed with two non-interacting fluids. In this work, we extend the formalism in Ref [1] by considering each fluid’s anisotropic pressure. Therefore, the total energy-momentum tensor is the sum of two non-interacting anisotropic fluids with different four-velocities. The velocity difference of both fluids denotes here by b where it comes from each of four-velocities under transformation rotation. Our result’s direct impact is that we can assess each fluid’s impact of anisotropic pressure in two fluids formalism in NS or other compact objects properties.