Dilation Dark Matter in Vaidya-De-Sitter Spacetime

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.