## Exact solutions for relativistic models.

##### Abstract

In this thesis we study spherically symmetric spacetimes related to the Einstein field equations. We consider only neutral matter and apply the Einstein field equations with isotropic pressures. Our object is to model relativistic stellar systems. We express the Einstein field equations and the condition of pressure isotropy in terms of Schwarzschild coordinates and isotropic coordinates. For Schwarzschild coordinates we consider the
transformations due to Buchdahl (1959), Durgapal and Bannerji (1983), Fodor (2000) and Tewari and Pant (2010). The condition of pressure isotropy is integrated and new exact solutions of the field equations are obtained utilizing the transformations of Buchdahl (1959) and Tewari and Pant (2010). These exact solutions are given in terms of elementary functions. For isotropic coordinates we can express the condition of pressure isotropy as a Riccati equation or a linear equation. An algorithm is developed that produces a new solution if a particular solution is known. The transformations reduce to a nonlinear Bernoulli equation in most instances. There are fundamentally three new classes of solutions to the condition of pressure isotropy.