  We consider a generalization of the Lemaitre-Tolman-Bondi (LTB) solutions by
keeping the LTB metric but replacing its dust matter source by an imperfect
fluid with anisotropic pressure $\Pi_{ab} $. Assuming that total matter-energy
density $\rho$ is the sum of a rest mass term, $\rhom$, plus a radiation
$\rhor=3p$ density where $p$ is the isotropic pressure, Einstein's equations
are fully integrated without having to place any previous assumption on the
form of $\Pi_{ab} $. Three particular cases of interest are contained: the
usual LTB dust solutions (the dust limit), a class of FLRW cosmologies (the
homogeneous limit) and of the Vaydia solution (the vacuum limit). Initial
conditions are provided in terms of suitable averages and contrast functions of
the initial densities of $\rhom, \rhor$ and the 3-dimensional Ricci scalar
along an arbitrary initial surface $t=t_i$. We consider the source of the
models as an interactive radiation-matter mixture in local thermal equilibrium
that must be consistent with causal Extended Irreversible Thermodynamics (hence
$\Pi_{ab} $ is shear viscosity). Assuming near equilibrium conditions
associated with small initial density and curvature contrasts, the evolution of
the models is qualitatively similar to that of adiabatic perturbations on a
matter plus radiation FLRW background. We show that initial conditions exist
that lead to thermodynamically consistent models, but only for the full
transport equation of Extended Irreversible Thermodynamics. These interactive
mixtures provide a reasonable approximation to a dissipative 'tight coupling'
characteristic of radiation-matter mixtures in the radiative pre-decoupling
era.
