A charged anisotropic well-behaved Adler-Finch-Skea solution Satisfying Karmarkar Condition

Abstract

In the present article, we discover a new well-behaved charged anisotropic solution of Einstein-Maxwell's field equations. We ansatz the metric potential $g_{00}$ of the form given by Maurya el al. (arXiv:1607.05582v1) with $n=2$. In their article it is mentioned that for $n=2$ the solution is not well-behaved for neutral configuration as the speed of sound is non-decreasing radially outward. However, the solution can represent a physically possible configuration with the inclusion of some net electric charged i.e. the solution can become a well-behaved solution with decreasing sound speed radially outward for a charged configuration. Due to the inclusion of electric charged the solution leads to a very stiff equation of state (EoS) with the velocity of sound at the center $v_{r0}^2=0.819, ~v_{t0}^2=0.923$ and the compactness parameter $u=0.823$ is closed to the Buchdahl limit 0.889. This stiff EoS support a compact star configuration of mass $5.418M_\odot$ and radius of $10.1 km$.