Expansion-free dissipative fluid spheres: Analytical models

We search exact analytical solutions of spherically symmetric dissipative fluid distributions satisfying the vanishing expansion condition (vanishing expansion scalar $\mathrm{\Theta }$). To do so we shall impose additional restrictions allowing the integration of the field equations. A detailed analysis of the obtained solutions, their prospective applications to astrophysical scenarios, as well as alternative approaches to obtain new solutions, are discussed.