A generalized Finch–Skea class one static solution

Abstract

In the present article, we discuss relativistic anisotropic solutions of Einstein field equations for the spherically symmetric line element under the class I condition. To do so we apply the embedding class one technique using Eisland condition. Within this approach, one arrives at a particular differential equation that links the two metric components e ν and e λ . In order to obtain the full space–time description inside the stellar configuration we ansatz the generalized form of metric component g rr corresponding to the Finch–Skea solution. Once the space–time geometry is specified we obtain the complete thermodynamic description i.e. the matter density ρ, the radial, and tangential pressures p r and p t , respectively. Graphical analysis shows that the obtained model respects the physical and mathematical requirements that all ultra-high dense collapsed structures must obey. The M–R diagram suggests that the solution yields stiffer EoS as parameter n increases. The M–I graph is in agreement with the concepts of Bejgar et al. (Mon Not R Astron Soc 364:635, 2005) that the mass at I max is lesser by few percent (for this solution ∼ 3 %) from M max . This suggests that the EoSs is without any strong high-density softening due to hyperonization or phase transition to an exotic state.