Generalized radiating stellar models with cosmological constant and electric charge.

Abstract

A general matter distribution, with the addition of the cosmological constant and electric charge, for the interior spacetime of a spherically symmetric radiating star undergoing gravitational collapse is considered in this investigation. The matching of the metric potentials and extrinsic curvature for the interior spacetime to the Vaidya exterior spacetime leads to the junction condition that relates the radial pressure to the heat flux. The presence of the cosmological constant and electric charge changes the nature of the problem significantly. Using Einstein-Maxwell field equations we express the junction condition as a Riccati equation in one of the metric potentials. In general this Riccati equation is not integrable. Special cases for particular matter distributions result in new classes of exact solutions to the Riccati equation. Previous results are also regained in this process. A transformation, called the horizon function, is then introduced to transform the Riccati equation into a simpler form. Several new classes of exact solutions are also found for the transformed Riccati equation. A new transformation called the generalized horizon function is introduced. This transformation preserves the form of the Riccati equation. The generalized horizon function leads to a transformed generalized Riccati equation. It is also possible to obtain earlier models by making assumptions on certain parameters. New models arise by restricting the values of parameters. The classes of solutions found can be given both implicitly and explicitly. The horizon function, and its generalization, can be obtained explicitly for all models.