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.