A generalised embedding class one static solution describing anisotropic fluid sphere

Abstract

In the present article, the Eiesland condition has been used to obtain a new solution for compact star model by considering a non-singular well behaved gravitational potential of the form $e^{\lambda (r)}=1+a r ^{2} [1+\tanh (br^{2}+c)]^{n}$ in the framework of anisotropic matter distribution. The solution so obtained is physically acceptable, which is exploited to compare the predicted masses and radii of known compact object as EXO 1785-248 ($M=1.3M_{\odot }$) for $n= 3$ to 15. Moreover, the obtained solution satisfies the causality condition, Herrera cracking criterion, Tolman-Oppenheimer-Volkoff (TOV) equation, and adiabatic index $\varGamma$ including all energy conditions. It is noted that the velocity of sound is increasing at $n=3$ and start decreasing when $n\ge 6$ which shows that the parameter $n$ plays an important role to describe a well-behaved solution for anisotropic compact object. The moment of inertia $(I)$ is also obtained by Bejger-Haensel formula for $n=3$ to 15. In addition to that, the maximum mass for the compact star has been discovered via. $M-R$ curve for different values of $n$.