A charged anisotropic well-behaved Adler–Finch–Skea solution satisfying Karmarkar condition

TLDR: In this paper, a new well-behaved charged anisotropic solution of the field equations was discovered, which can represent a physically possible configuration with the inclusion of some net electric charge, i.e. the solution can become a wellbehaved solution with decreasing sound speed radially outward.

Abstract: In the present paper, we discover a new well-behaved charged anisotropic solution of Einstein–Maxwell’s field equations. We ansatz the metric potential g00 of the form given by Maurya el al. (Eur. Phys. J. C 76(2) (2016) 693) with n = 2. In their paper, it is mentioned that for n = 2, the solution is not well-behaved for neutral configuration as the speed of sound is nondecreasing radially outward. However, the solution can represent a physically possible configuration with the inclusion of some net electric charge, 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 charge, the solution leads to a very stiff equation-of-state (EoS) with the velocity of sound at the center vr02 = 0.819, vt02 = 0.923 and the compactness parameter u = 0.823 is close to the Buchdahl limit 0.889. This stiff EoS support a compact star configuration of mass 5.418M⊙ and radius of 10.1km.