Matter field quantum fluctuations in a Bianchi II metric

It is pointed out that a three-dimensional metric space of type II according to the Bianchi classification can be obtained by a Kaluza-Klein construction from a flat two-dimensional space with a homogeneous magnetic field. Quantum fluctuations of matter fields in this background metric turn out to be closely related to those of charged fields in a homogeneous magnetic field, and the vacuum energy can be summed explicitly. The analogous construction involving an electric field leads to a metric decaying by pair creation