[01] Mohammad Abu Kauser, Department of Mathematics, Chittagong University of Engineering and Technology, Chattogram, Bangladesh. [02] Quamrul Islam, Jamal Nazrul Islam Research Center for Mathematical and Physical Sciences, University of Chittagong, Chattogram, Bangladesh.

For the highly nonlinearity conditions, it is so much difficult to obtain exact solutions of Einstein’s equations. Many authors have been working on the investigation of exact solutions of Einstein’s equations. There are a fair number of static spherically symmetric exact solutions of Einstein’s equations. One of these solutions, Schwarzschild uniform density solution is unphysical. In this paper, we have demonstrated that field equations for static spherically anisotropic spacetimes can be reduced to Riccati type differential equations. Moreover, we have presented three new techniques for finding static spherically symmetric anisotropic solutions of Einstein’s equations. Using one of these techniques, a class of new solutions is generated. The solution is realistic and physically acceptable.

Radial Pressure, Tangential Pressure, Energy Density, Isotropic Solution, Anisotropic Solution, Hydrostatic Equilibrium, Polytrope Index

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