A generating function and new exact solutions for geodesic matter

Abstract

In this paper we study a geodesic radiating stellar model in which the Einstein field equations contain a cosmological constant and electric charge. Firstly, we study the boundary condition by introducing a generating function that is directly related to the horizon function. This generating function transforms the boundary condition into an algebraic equation which is solvable. New classes of exact solutions can be obtained by specifying a form for the generating function. It is possible to express physical quantities such as the mass and compactness factor in terms of the generating function. We also regain earlier results with only electric charge in this process. Secondly, we transformed the boundary condition into a second order differential equation in terms of the generating function. By specifying certain parameters we solved the boundary condition by direct integration and obtained a new special class of exact solutions in terms of confluent hypergeometric functions.