A generalized Finch–Skea class one static solution

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 $$e^{\nu }$$ and $$e^{\lambda }$$ . 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 $$\rho $$ , 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 $$\sim 3\%$$ ) 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.

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