Static spacetimes haunted by a phantom scalar field III: asymptotically (A)dS solutions

TL;DR

This paper constructs and analyzes asymptotically (A)dS solutions in higher-dimensional Einstein-phantom-scalar systems, revealing new black hole and wormhole configurations with detailed global structures and scalar potentials.

Contribution

It introduces a method to generate asymptotically (A)dS solutions from known seed solutions, expressing scalar potentials via superpotentials, and explores their global properties and parameter domains.

Findings

Identified conditions for black hole and wormhole solutions.

Presented new traversable wormholes connecting different (A)dS critical points.

Detailed the global structure and parameter space of the solutions.

Abstract

The static and spherically symmetric solutions in $n(\ge 4)$-dimensional Einstein-phantom-scalar system fall into three family: (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.