On the wave equation in spacetimes of Goedel type

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.

arXiv commentSignificantly updated version, also including discussion of the Som-Raychaudhuri (flat) case; Chapter in "Gödel-type spacetimes: history and new developments", Annals of the Kurt Gödel Society, ed. M. Scherfner and M. Plaue (2010)