A comparative study on generalized model of anisotropic compact star satisfying the Karmarkar condition

TLDR: In this paper, a non-singular solution satisfying the Karmarkar condition is presented, which yields finite values of metric potentials, density, pressure, redshift, etc.

Abstract: A new solution satisfying the Karmarkar condition is presented here. We were first to have discovered a hypergeometric function metric potential representing embedding class I spacetime. This new solution yields finite values of metric potentials, density, pressure, redshift, etc. and hence a non-singular solution. The solution is well behaved with respect to the parameter $$n=12$$ to $$n=24$$ corresponding to a stable configuration of mass $$2.01M_\odot $$ and radius 9.1 km. The internal properties of the solution are very different for $$n=12$$ to $$n=24$$ ; however, the total mass and radius is independent of the parameter n. The energy conditions are also holds good by the solution which thus can represent a physically viable matter distribution. The equilibrium condition and stability are also discussed through TOV-equation, cracking method and $$\Gamma >4/3$$ . The static stability criterion is also well satisfied and the turning point corresponds to $$4.46M_\odot $$ for a radius of 9.1 km.