Gravitational Potential Effects on Shearing Geodesic Fluid Solutions of Einstein's Equations

In this paper we analyze spherically symmetric shearing geodesic fluids in gravitational potential when the interior space expanding shearing fluid particles are traveling in geodesic motion. We find two analytic exact solutions of Einstein's field equations (EFE) in terms of isotropic pressure, energy density, stress tensor, and heat flux vector. A systematic approach enables us to write the junction condition as a Riccati equation. We obtain one new solution depending on arbitrary functions (using separation of variables) and we discuss its physical significance in the stellar modeling.