A New Classes of Solutions of the Einstein-Maxwell Field Equations with Pressure Anisotropy

In this paper, we present a class of exact solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere.  The field equations are integrated by specifying the forms of the electric field, anisotropic factor, and one of the gravitational potentials which are physically reasonable. By reducing the condition of pressure isotropy to a linear, second order differential equation which can be solved in general, we show that it is possible to obtain closed-form solutions for a specific range of model parameters.  The solution is regular, well behaved and complies with all the requirements of a realistic stellar model. An interesting feature of the new class of solutions is that one can easily switch off the electric and/or anisotropic effects in this formulation. Consequently, we regain some of the earlier solutions.

Keywords:

Relativistic star , exact solutions , field equations , astrophysical objects