de Sitter black hole with a conformally coupled scalar field in four dimensions

TL;DR

This paper presents a new four-dimensional de Sitter black hole solution coupled with a conformal scalar field, including charged variants, highlighting singularities and bounded scalar self-interaction.

Contribution

It introduces a novel exact black hole solution with conformal scalar coupling in de Sitter space, including charged cases, and analyzes the scalar field behavior and self-interaction bounds.

Findings

Presence of a curvature singularity at the origin.

Scalar field diverges inside the event horizon.

Charged solution with fixed charge-to-mass ratio.

Abstract

A four-dimensional black hole solution of the Einstein equations with a positive cosmological constant, coupled to a conformal scalar field, is given. There is a curvature singularity at the origin, and scalar field diverges inside the event horizon. The electrically charged solution, which has a fixed charge-to-mass ratio is also found. The quartic self-interacting coupling becomes bounded in terms of Newton's and the cosmological constants.