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On the wave equation in spacetimes of Goedel type

P. Marecki
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Abstract

We analyze the d'Alembert equation in the Goedel-type spacetimes with spherical and Lobachevsky sections (with sufficiently rapid rotation). By separating the $t$ and $x_3$ dependence we reduce the problem to a group-theoretical one. In the spherical case solutions have discrete frequencies, and involve spin-weighted spherical harmonics. In the Lobachevsky case we give simple formulas for obtaining all the solutions belonging to the $D^\pm_\la$ sectors of the irreducible unitary representations of the reduced Lorentz group. The wave equation enforces restrictions on $\la$ and the allowed (here: continuous) spectrum of frequencies.

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P. Marecki. 2012-01-24. On the wave equation in spacetimes of Goedel type. https://arxiv.org/abs/gr-qc/0703018

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