Isotropic stellar model in mimetic theory

Abstract

We investigate how to derive an isotropic stellar model in the frame of mimetic gravitational theory. Recently, this theory has gained big interest due to its difference from Einstein’s general relativity (GR), especially in the domain non-vacuum solutions. In this regard, we apply the field equation of mimetic gravitational theory to a spherically symmetric ansatz and obtain an over determined system of non-linear differential equations in which the number of differential equations is less than the unknown functions. To overcome the over determined system we suppose a specific form of the temporal component of the metric potential, g_{tt}, and assume the vanishing of the anisotropic condition to derive the form of the spatial component of the metric, g_{rr}. In this regard, we discuss the possibility to derive a stellar isotropic model that is in agreement with observed pulsars. To examine the stability of the isotropic model we use the Tolman–Oppenheimer–Volkoff equation and the adiabatic index. Moreover, we test the model using a wide range of observed values of masses and radii of pulsars and show that they fit in a good way.