Friedmann-like collapsing model of a radiating sphere with heat flow

This paper considers a spherical body consisting of a fluid with heat flow which radiates in its exterior a null fluid described by the outgoing Vaidya's metric. A Friedmann-like exact solution of the interior Einstein field equations is given. It is proved that this solution, matched with the outgoing Vaidya matric, represents a physically reasonble collapsing model which, when the heat flow is switched off, reduces to the well-known collapsing model with dust. The proposed model has the remarkable property that even if the heat flow is small, the horizon will never be formed because, before this happens, the collapsing body will be destroyed by opposite gradients of pressure.