Physical viability of fluid spheres satisfying the Karmarkar condition

Abstract: We obtain a new solution of the TOV-equation for an anisotropic fluid distribution by imposing the Karmarkar condition. In order to close the system of equations we postulate an interesting form for the grr gravitational potential which allows us to solve for gtt metric component via the Karmarkar condition. We demonstrate that the new interior solution has well-behaved physical attributes and can be utilized to model relativistic static fluid spheres. By using observational data sets for the radii and mass-to-radius relations for compact stars such as 4U 1538-52, LMC X-4 and PSR J1614- 2230 we show that our solution describes these objects to a very good degree of accuracy. The physical plausibility of the solution depends on a parameter $c$ for a particular star. For 4U 1538-52 the solution behaves well for $0.1574 \le c \le 0.46$ which corresponds to $1 \ge v^2_{r0} \ge 0:13$, $0.91 \ge v^2_{t0}\ge 0.04$ and $17.8 \ge \Gamma_0 \ge 3.8$. For LMC X-4 the solution behaves well for $0.1235 \le c \le 0.35$ which corresponds to $0.99 \ge v^2_{r0} \ge 0.15$, $0.91 \ge v^2_{t0}\ge 0.06$ and $15.35 \ge \Gamma_0 \ge 3.35$. Our model approximates the pulsar PSR J1614-2230 for $0.05 \le c \le 0.13$ which corresponds to $1 \ge v^2_{r0}\ge 0.21$, $0.94 \ge v^2_{t0} \ge 0.13$ and $8.34 \ge \Gamma_0 \ge 2.34$. Our observations of the behavior of the thermodynamical and physical variables of these compact objects lead us to conclude that the parameter c plays an important role in determining the equation of state of the stellar material. It is apparent that smaller values of c lead to stiffer equation of states and vice-versa.