An anti-Schwarzshild solution: wormholes and scalar-tensor solutions

We investigate a static solution with an hyperbolic nature, characterised by a pseudo-spherical foliation of space. This space-time metric can be perceived as an anti-Schwarzschild solution, and exhibits repulsive features. It belongs to the class of static vacuum solutions termed "a degenerate static solution of class A". In the present work we review its fundamental features, discuss the existence of generalised wormholes, and derive its extension to scalar-tensor gravity theories in general.