A study on the effect of anisotropy under Finch-Skea geometry

Abstract: The popularity of the Finch-Skea ansatz to describe relativistic stellar model have encouraged us to study the analytic solutions of the Einstein field equation. We have presented a class of exact solutions to the field equations after considering the corresponding two cases: (i) positive value of anisotropic parameter, and (ii) absence of any anisotropy. Smooth matching of the interior solutions with the Schwarzschild exterior solution helped us to determine constants. The physical features of the solutions thus obtained have been studied both graphically and numerically with the specific pulsar $4U~1608-52$ (Mass = $1.57^{+0.30}{-0.29}~M\odot$ and radius = $9.8\pm 1.8~km$). The stability conditions for the model have also been discussed, however the model is found to be stable for zero anisotropy.