Electromagnetic, neutrino and gravitational fields in the Kasner space-time with rotational symmetry

Abstract

The Hertz-Debye superpotential formalism has been applied to study the behaviour of the perturbative zero rest-mass fields, namely, the electromagnetic, massless neutrino and gravitational fields in the rotationally symmetric Kasner Universe. The formalism yields a single decoupled equation for the superpotential in each of the three cases. A considerable amount of information is obtained from these equations themselves and the equations are subjected to various methods of solution. The effects of anisotropy of the Kasner space-time on the superposed fields are analysed. The relative behaviour of the three fields is studied with the similarities and differences in their evolution being highlighted. Finally in the geometric optics approximation the propagation of the fields is compared with the null geodesics.