Narrow Results

In this paper, we present a model of a compact relativistic anisotropic star in the presence of an electric field. In order to obtain an exact solution of the Einstein–Maxwell field equations, we assume that the stellar material inside the star obeys a Chaplygin equation of state which is a nonlinear relationship between the radial pressure and the matter density. Using Tolman’s metric potential for $g_{rr}$, we obtain the other metric co-efficient by employing the Karmarkar condition which is a necessary and sufficient condition for the interior spacetime of our model to be of embedding class I. Our stellar model is free from central singularity and obeys all the conditions for a realistic stellar object.

In the present paper, we have constructed a new relativistic anisotropic compact star model having a spherically symmetric metric of embedding class one. Here we have assumed an arbitrary form of metric function $e^{\lambda }$ and solved the Einstein’s relativistic field equations with the help of Karmarkar condition for an anisotropic matter distribution. The physical properties of our model such as pressure, density, mass function, surface red-shift, gravitational redshift are investigated and the stability of the stellar configuration is discussed in details. Our model is free from central singularities and satisfies all energy conditions. The model we present here satisfy the static stability criterion, i.e. $dM/d{\rho }_c>0$ for $0\le {\rho }_c\le 4.04\times 10^{17}$g/cm³ (stable region) and for ${\rho }_c\ge 4.04\times 10^{17}$g/cm³, the region is unstable i.e. $dM/d{\rho }_c\le 0$.