Relativistic compact stars in the Kuchowicz spacetime

TL;DR

This paper derives a new relativistic model for anisotropic, charged compact stars using the Kuchowicz spacetime, demonstrating its applicability to neutron and quark stars with detailed mass-radius relations.

Contribution

It introduces a novel anisotropic charged solution in Kuchowicz spacetime, applicable to modeling various ultra-dense stars with detailed parameter analysis.

Findings

Model can describe stable ultra-dense stars like neutron and quark stars.

Increased charge and anisotropy improve stability of star configurations.

Maximum mass decreases with higher surface density, indicating softer equations of state.

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.