Asymptotically (anti) de Sitter Black Holes and Wormholes with a Self Interacting Scalar Field in Four Dimensions

TL;DR

This paper presents a variety of exact solutions in Einstein gravity with a conformally coupled scalar field, including regular black holes and wormholes connecting different (anti) de Sitter regions, supported by regular scalar fields.

Contribution

It introduces new exact solutions for black holes and wormholes with a self-interacting scalar field in four dimensions, highlighting their regularity and connection between different cosmological constant regions.

Findings

Regular black holes with no singularities inside or outside the horizon.

Existence of topological wormholes connecting different (anti) de Sitter spaces.

Solutions supported by everywhere regular scalar fields.

Abstract

The aim of this paper is to report on the existence of a wide variety of exact solutions, ranging from black holes to wormholes, when a conformally coupled scalar field with a self interacting potential containing a linear, a cubic and a quartic self interaction is taken as a source of the energy-momentum tensor, in the Einstein theory with a cosmological constant. Among all the solutions there are two particularly interesting. On the one hand, the spherically symmetric black holes when the cosmological constant is positive; they are shown to be everywhere regular, namely there is no singularity neither inside nor outside the event horizon. On the other hand, there are spherically symmetric and topological wormholes that connect two asymptotically (anti) de Sitter regions with a different value for the cosmological constant. The regular black holes and the wormholes are supported by everywhere regular scalar field configurations.