Motivated by a recent report by Biwas and Bose (Phys Rev D 99:104002, 2019) that the observations of GW170817 to constrain the extent of pressure anisotropy in neutron stars within Bower–Liang anisotropic model, we systematically study the effects of anisotropic pressure on properties of the neutron stars with hyperons. The equation of state is calculated using the relativistic mean-field model with a BSP parameter set to determine nucleonic coupling constants and by using SU(6) and hyperon potential depths to determine hyperonic coupling constants. We investigate three models of anisotropic pressure known in literature namely Bowers and Liang (Astrophys J 88:657, 1974), Horvat et al. (Class Quant Grav 28:025009, 2011), and Cosenza et al. (J Math Phys (NY) 22:118, 1981). The reliability of the equation of state used is checked by comparing the parameters of the corresponding EOS to recent experimental data. The mass–radius, moment of inertia, and tidal deformability results of Bowers–Liang, Horvat et al., and Cosenza et al. anisotropic models are compared to the corresponding recent results extracted from the analysis of some NS observation data. We have found that the radii predicted by anisotropic NS are sensitive to the anisotropic model used and the results obtained by using the model proposed by Horvat et al. with anisotropic free parameter $$\varUpsilon ~\approx -$$Υ≈- 1.15 are relative compatible with all taken constraints.

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The role of scalar boson exchange as a mediator of the fermionic dark particle interaction and the mass of dark particle on the bulk properties of fermionic dark stars including their moment of inertia and tidal deformability are studied. We have found that the role of the attractive nature of the scalar boson exchange and the fermionic dark particle mass can control the stiffness of the fermionic dark star equation of state. By increasing the strength of scalar boson coupling, the fermionic dark star becomes more compact. As a consequence, if scalar boson exchange contribution is included the compactness of a dark star can exceed C=0.22. We also compare the fermionic dark stars moment of inertia and tidal deformability to those of neutron stars (with and without hyperons in neutron star core) predicted by relativistic mean field model. It is evidence that the properties of both types of stars are quite different. We also have found that the universal I-Love relation in fermionic dark stars is not affected by scalar boson exchange contribution and the fermionic dark particle mass. Possible observations of fermionic dark stars are also discussed.

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.

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