New anisotropic star solutions in mimetic gravity

Abstract

We extract new classes of anisotropic solutions in the framework of mimetic gravity, by applying the Tolman–Finch–Skea metric and a specific anisotropy not directly depending on it, and by matching smoothly the interior anisotropic solution to the Schwarzschild exterior one. Then, in order to provide a transparent picture we use the data from the 4U 1608-52 pulsar. We study the profile of the energy density, as well as the radial and tangential pressures, and we show that they are all positive and decrease toward the center of the star. Furthermore, we investigate the anisotropy parameter and the anisotropic force that are both increasing functions of the radius, which implies that the latter is repulsive. Additionally, by examining the radial and tangential equation-of-state parameters, we show that they are monotonically increasing, not corresponding to exotic matter. Concerning the metric potentials, we find that they have no singularity, either at the center of the star or at the boundary. Furthermore, we verify that all energy conditions are satisfied, we show that the radial and tangential sound speed squares are positive and sub-luminal, and we find that the surface redshift satisfies the theoretical requirement. Finally, in order to investigate the stability we apply the Tolman–Oppenheimer–Volkoff equation, we perform the adiabatic index analysis, and we examine the static case, showing that in all cases the star is stable.