On homothetic Killing vectors in stationary axisymmetric vacuum spacetimes

Abstract

In this paper, we consider homothetic Killing vectors in the class of stationary axisymmetric vacuum (SAV) spacetimes, where the components of the vectors are functions of the time and radial coordinates. In this case, the component of any homothetic Killing vector along the [Formula: see text] direction must be constant. First, it is shown that either the component along the radial direction is constant or we have the proportionality [Formula: see text], where [Formula: see text]. In both cases, complete analyses are carried out and the general forms of the homothetic Killing vectors are determined. The associated conformal factors are also obtained. The case of vanishing twist in the metric, i.e. [Formula: see text] is considered and the complete forms of the homothetic Killing vectors are determined, as well as the associated conformal factors.