Anisotropic fluid spheres of embedding class one using Karmarkar condition

Abstract

We obtain a new anisotropic solution for spherically symmetric spacetimes by analyzing the Karmarkar embedding condition. For this purpose we construct a suitable form of one of the gravitational potentials to obtain a closed form solution. This form of the remaining gravitational potential allows us to solve the embedding equation and integrate the field equations. The resulting new anisotropic solution is well behaved, which can be utilized to construct realistic static fluid spheres. Also we estimated the masses and radii of fluid spheres for LMC X-4, EXO 1785-248, PSR J1903+327 and 4U 1820-30 by using observational data set values. The masses and radii obtained show that our anisotropic solution can represent fluid spheres to a very good degree of accuracy. The physical validity of the solution depends on the parameter values of a, b and c. The solution is well behaved for the wide range of parameters values 0.00393≤a≤0.0055, 0.0002≤b≤0.0025 and 0.0107≤c≤0.0155. The range of corresponding physical parameters for the different compact stars are 0.3266≤vr0≤0.3708, 0.1583≤vt0≤0.2558, 0.3256≤zs≤0.4450 and 4.3587≤Γ0≤5.6462.