The use of generating techniques for space-times with two non-null commuting Killing vectors in vacuum and stiff perfect fluid cosmological models

Abstract

The SL(2) formalism of Kinnersley and Chitre (1978) for generating techniques in stationary axisymmetric vacuum space-times is adapted to work for space-times with two spacelike commuting Killing vectors. The Kinnersley-Chitre formalism is known to be explicitly related to the inverse scattering transformation of Belinskii and Zakharov (1979) which has already been applied in both types of above mentioned space-times. Using the hyperbolic versions of various Kinnersley-Chitre transformations the interrelation between various vacuum cosmological solutions is obtained. For each solution the Kinnersley-Chitre generating function FAB(t) and corresponding Belinskii-Zakharov eigenfunction psi ( lambda ) is given. These vacuum solutions are then converted to scalar field/stiff perfect fluid solutions using the algorithm of Wainwright, Ince and Marshman (1979).