Relativistic compact stars in the Kuchowicz spacetime

Abstract: We present an anisotropic charged analogue of Kuchowicz (1971) solution of the general relativistic field equations in curvature coordinates by using simple form of electric intensity $E$ and pressure anisotropy factor $\Delta$ that involve charge parameter $K$ and anisotropy parameter $\alpha$ respectively. Our solution is well behaved in all respects for all values of $X$ ( $X$ is related to the radius of the star ) lying in the range $0< X \le 0.6$, $\alpha$ lying in the range $0 \le \alpha \le 1.3$, $K$ lying in the range $0< K \le 1.75$ and Schwarzschild compactness parameter "$u$" lying in the range $0< u \le 0.338$. Since our solution is well behaved for a wide range of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We present some models of super dense quark stars and neutron stars corresponding to $X=0.2,~\alpha=0.2$ and $K=0.5$ for which $u_{max}=0.15$. By assuming surface density $\rho_b=4.6888\times 10^{14}~ g/cc$ the mass and radius are $0.955 M_\odot$ and $9.439 km$ respectively. For $\rho_b=2.7\times 10^{14}~ g/cc$ the mass and radius are $1.259 M_\odot$ and $12.439 km$ respectively and for $\rho_b=2\times 10^{14}~ g/cc$ the mass and radius are $1.463 M_\odot$ and $14.453 km$ respectively. It is also shown that inclusion of more electric charge and anisotropy enhances the static stable configuration under radial perturbations. The $M-R$ graph suggests that the maximum mass of the configuration depends on the surface density {\bf i.e. with the increase of surface density} the maximum mass and corresponding radius decrease. This may be because of existence of exotic matters at higher densities that soften the EoSs.