  We construct new solutions of the vacuum Einstein field equations in four
dimensions via a solution generating method utilizing the SL(2,R) symmetry of
the reduced Lagrangian. We apply the method to an accelerating version of the
Zipoy-Voorhees solution and generate new solutions which we interpret to be the
accelerating versions of the Zipoy-Voorhees generalisation of the Taub-NUT
solution (with Lorentzian signature) and the Zipoy-Voorhees generalisation of
the Eguchi-Hanson solitons (with Euclidean signature). As an intermediary in
the solution-generating process we obtain charged versions of the accelerated
Zipoy-Voorhees-like families of solutions. Finally we present the accelerating
version of the Taub-NUT solution and discuss its properties.
