Radiation Damping in FRW Space-times with Different Topologies

TL;DR

This paper investigates how the topology and connectedness of flat FRW space-times influence the energy evolution of radiating systems, revealing exponential damping in non-compact space and oscillatory patterns in compact spaces.

Contribution

It provides a comparative analysis of energy damping behaviors in different flat FRW topologies, clarifies previous misinterpretations, and discusses underlying reasons for divergent energy evolution patterns.

Findings

Exponential energy damping in Euclidean space.

Oscillatory energy patterns in compact flat manifolds.

Clarification of Wolf's results on flat 3-manifolds.

Abstract

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 3-manifold ${\cal R}^3$ and six topologically non-equivalent flat orientable compact multiply connected Riemannian 3-manifolds. An exponential damping of the energy $E(t)$ is present in the ${\cal R}^3$ case, whereas for the six compact flat 3-spaces it is found basically the same pattern 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 $E(t)$. Likely reasons for this divergent behavior of $E(t)$ in these compact flat 3-manifolds are discussed and further developments are indicated. A misinterpretation of Wolf's results regarding one of the six orientable compact flat 3-manifolds is also indicated and rectified.