## 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.