Abstract.
We have explored a family of new solutions satisfying Einstein’s field equations and Karmarkar condition. We have assumed an anisotropic stress-tensor with no net electric charge. Interestingly, the new solutions yield zero values of all the physical quantities for all even integer \(n > 0\). However, for all \(n >0\) (\(n \neq \) even numbers) they yield physically possible solutions. We have tuned the solution for neutron star Vela X-1 so that the solutions matches the observed mass and radius. For the same star we have extensively discussed the behavior of the solutions. The solutions yield a stiffer equation of state for larger values of n since the adiabatic index increases and speed of sound approaches the speed of light. It is also found that the solution is physically possible for Vela X-1 if \(1.8 \leq n < 7\) (with \(n\neq 2,4,6\)). All the solutions for \(n \geq 7\) violates the causality condition and all the solutions with \(0 < n < 1.8\) lead to complex values of transverse sound speed \( v_{t}\). The range of well-behaved n depends on the mass and radius of compact stars.
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Newton Singh, K., Pant, N., Tewari, N. et al. Embedded class solutions compatible for physical compact stars in general relativity. Eur. Phys. J. A 54, 77 (2018). https://doi.org/10.1140/epja/i2018-12510-x
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DOI: https://doi.org/10.1140/epja/i2018-12510-x