Neutrinos in the Kerr and Robertson-Walker geometries

Abstract

The perturbative behaviour of neutrinos is examined in the framework of the Hertz potential formalism in two important space-times, namely the Kerr and Robertson-Walker space-times. In particular, the angular functions of the neutrino field are studied in detail on the background of the Kerr geometry. It is found that the properties of the solution depend crucially on the value of the separation constant Q defined in the text. It is found that the Robertson-Walker model (k=+1) harbours a repulsive effective potential for neutrinos. The behaviour of the neutrinos in the cases of the spherically collapsing dust interior and the k=-1 Robertson-Walker model can be deduced from the k=+1 case. Also exact solutions in term of known functions are obtained for the neutrino perturbations for the k=0 case. In the geometric optics limit ( omega M»1) all the results agree with the classical ones obtained in the null geodesic formalism.