  The exterior of a relativistic star can be modelated with the Vaidya
radiating metric. It is started from the generalized Vaidya metric that allows
a type II fluid and studied the conditions of generating new analytical
solutions of the Einstein's field equations. It is shown that the mass
parameter solution gives the classical de Sitter universe in the static case
and the extended de Sitter metric coupled with a dilation scalar field in the
time-dependent case. It is concluded that in the time-dependent case the
atmosphere of a relativistic star consists on an anisotropic string fluid
coupled with a dark matter null fluid and interpreted the scalar field as the
particle that produces the dark matter.
