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Compact Relativistic Stars under Karmarkar Condition

A class of new solutions for Einstein's field equations, by choosing the ansatz $e^{λ(r)}=\frac{1+ar^{2}}{1+br^{2}}$ for metric potential, are obtained under Karmarkar condition. It is found that a number of pulsars like 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, PSR J1614-2230, Cen X-3 can be accomodated in this model. We have displayed the nature of physical parameters and energy conditions throughout the distribution using numerical and graphical methods for a particular pulsar 4U 1820-30 and found that the solution satisfies all physical requirements.