Topological Reverberations in Flat Space-times

Details Topological Reverberations in Flat Space-times Topological Reverberations in Flat Space-times

1999-03-09

arxiv.org/abs/gr-qc/9903037v2

Int.J.Mod.Phys. A15 (2000) 4141-4162

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, 4 figures, REVTEX; Added five references and inserted clarifying details. Version to appear in Int. J. Mod. Phys. A

Scientific paper

10.1142/S0217751X0000208X

We study the role played by multiply-connectedness in the time evolution of the energy E(t) of a radiating system that lies in static flat space-time manifolds M_4 whose t=const spacelike sections M_3 are compact in at least one spatial direction. The radiation reaction equation of the radiating source is derived for the case where M_3 has any non-trivial flat topology, and an exact solution is obtained. We also show that when the spacelike sections are multiply-connected flat 3-manifolds the energy E(t) exhibits a reverberation pattern with discontinuities in the derivative of E(t) and a set of relative minima and maxima, followed by a growth of E(t). It emerges from this result that the compactness in at least one spatial direction of Minkowski space-time is sufficient to induce this type of topological reverberation, making clear that our radiating system is topologically fragile. An explicit solution of the radiation reaction equation for the case where M_3 = R^2 x S^1 is discussed, and graphs which reveal how the energy varies with the time are presented and analyzed.

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