Static spacetimes haunted by a phantom scalar field. III. Asymptotically (A)dS solutions

The static and spherically symmetric solutions in the n(>= 4)-dimensional Einstein-phantom-scalar system fall into three families: (i) the Fisher solution, (ii) the Ellis-Gibbons solution, and (iii) the Ellis-Bronnikov solution. We exploit these solutions as seed to generate a bunch of corresponding asymptotically (A)dS spacetimes, at the price of introducing the potential of the scalar field. Despite that the potentials are different for each solution, each potential is expressed in terms of the superpotential as in supergravity. We discuss the global structure of these solutions in detail and spell out the domain of parameters under which each solution represents a black hole/wormhole. The Ellis-Bronnikov class of solutions presents novel examples of spherical traversable wormholes that interpolate two different (A)dS critical points of the (super)potential.

Automated summary

The static and spherically symmetric solutions in the n(≥4)-dimensional Einstein-phantom-scalar system can be classified into three families: the Fisher solution, the Ellis-Gibbons solution, and the Ellis-Bronnikov solution. These solutions are used as seeds to generate corresponding asymptotically (A)dS spacetimes by introducing the potential of the scalar field. Despite having different potentials, each potential is expressed in terms of the superpotential as in supergravity. Specifically, the novel examples of spherical traversable wormholes in the Ellis-Bronnikov class of solutions interpolate two different (A)dS critical points of the (super)potential.