Generalized horizon functions for radiating matter

Abstract

In this study, we consider a general spherically symmetric radiating matter distribution containing the cosmological constant and electric charge. We show that the boundary condition for the bounded matter distribution relating the radial pressure to the heat flow is a Riccati equation. We find a new transformation for the stellar boundary condition called the generalized horizon function since it is related to the formation of horizons during collapse. The generalized horizon function leads to a new equation which preserves the structure of the Riccati equation that governs the evolution of the boundary. Several new families of exact solutions, both implicit and explicit, to the transformed boundary condition are found. It is important to observe that the horizon function can be given explicitly in all cases. Results of previous studies arise as special cases of our general analysis.