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A charged anisotropic well-behaved Adler-Finch-Skea solution satisfying Karmarkar condition. (English) Zbl 1371.85006

Summary: In the present paper, 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 S. K. Maurya et al. [“Generalised model for anisotropic compact stars”, Eur. Phys. J. C 76, No. 12, Article No. 693, (2016; doi:10.1140/epjc/s10052-016-4527-5)] 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 \(v_{r0}^2=0.819\), \(v_{t0}^2=0.923\) 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 5.418 \(M_\odot\) and radius of 10.1 km.

MSC:

85A15 Galactic and stellar structure
83C22 Einstein-Maxwell equations
83C15 Exact solutions to problems in general relativity and gravitational theory

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