We study the one-particle properties of the t-J model within the framework of Vollhardt's dynamical mean field theory. By introducing an AB-sublattice structure we explicitly allow for a broken symmetry for the spin degrees of freedom and are thus able to calculate the one-particle spectral function in the antiferromagnetic phase. We observe surprisingly rich structures in the one-particle density of states for T < T N at finite doping up to 15%. These structures can be related to the well known results for one single hole in the Néel background. We are thus able to establish the relevance of this at a first sight academic limit to physical properties of the t-J model with a finite density of holes in the thermodynamical limit.