Generalized geodesic radiating models

Abstract

The Einstein field equations and junction conditions are studied for a radiating object in which particles are travelling in geodesic motion. We consider the general case including the effects of gravity, the cosmological constant and the electromagnetic field. The boundary condition is shown to be a Riccati equation in general. A transformation reduces the boundary condition to a simpler equation. Several families of new exact solutions are found, both explicitly and implicitly. The exact solutions can be written in terms of elementary functions, elliptic integrals and Gaussian hypergeometric functions. We find that the cosmological constant and charge affects the gravitational behaviour of the model. We identify earlier models as special cases in this analysis.