Israel-Wilson-Perjes metrics in a theory with a dilaton field

Abstract

We are interested in the charged dust solutions of the Einstein field equations in stationary and axially symmetric spacetimes and inquire if the naked singularities of the Israel-Wilson-Perjes (IWP) metrics can be removed. The answer is negative in four dimensions. We examine whether this negative result can be avoided by adding scalar or dilaton fields. We show that IWP metrics also arise as solutions of the Einstein-Maxwell system with a stealth dilaton field. We determine the IWP metrics completely in terms of one complex function satisfying the Laplace equation. With the inclusion of the stealth dilaton field, it is now possible to add a perfect fluid source. In this case, the field equations reduce to a complex cubic equation. Hence, this procedure provides interior solutions to each IWP metric, and it is possible to cover all naked singularities inside a compact surface where there is matter distribution.