Radiation damping in FRW space-times with different topologies

We study the role played by the compactness and the degree of connectedness in the time evolution of the energy of a radiating system in the Friedmann-Robertson-Walker (FRW) space-times whose $t=$const spacelike sections are the Euclidean three-manifold ${\mathcal{R}}^3$ and six topologically nonequivalent flat orientable compact multiply connected Riemannian three-manifolds. An exponential damping of the energy $E\left(t\right)\mathrm{}$ is present in the ${\mathcal{R}}^3$ case, whereas for the six compact flat three-spaces basically the same pattern is found for the evolution of the energy, namely, relative minima and maxima occurring at different times (depending on the degree of connectedness) followed by a growth of $E\left(t\right)\mathrm{}$. Likely reasons for this divergent behavior of $E\left(t\right)\mathrm{}$ in these compact flat three-manifolds are discussed and further developments are indicated. A misinterpretation of Wolf’s results regarding one of the six orientable compact flat three-manifolds is also indicated and rectified.