Generalized Gödel Universe with Heavy Photons

Abstract

An exact solution of EINSTEIN'S field equations with cosmological constant coupled with the field equations of a massive vector field is given. The model has zero expansion and shear, but nonvanishing constant rotation.Es wird cine strenge Losung des EINSTEIN-PRocA-Systems mit kosmologischern Glied angegeben. Die Losung weist keine Expansion und Scherung, aber eine konstante Rotation auf. Einstein-Proca equations with cosmological constantPROCA'S field equations (e.g. IWANENKO and SOKOLOV 1953) FrE + p2AP = o were interpreted differently in the past. We refer here to the interpretation of these equations by heavyphotons, which was the cause for controverses in the last time (e.g. TREDER 1977). Further we point to the interpretation by massive vector mesons. In particular, it was shown by TAUBER (1969) that massive vector mesons cannot be described phenomenologically by a perfect fluid in terms of a pressure and density only, but involves at least an additional term describing stresses in the energy-momentum tensor. All things considered, it seems desirable to investigate the interaction of heavy photons or massive vector mesons with the gravitational field. Here we want to give an exact solution of PROCA'S equations (I)-(4) coupled with EINSTEIN'S equationswhere A is the cosmological constant. We use throughout the space-like-convention by MISNER, THORNE and WHEELER (1973). Equations (5) can be also written in the formThe system (I), (2) can be only integrated, when the condition is fulfilled.A f a = o Generalized Godel universe and the field equationsStarting point is a line element of the form