Exact Black-Hole Solution With Self-Interacting Scalar Field

TL;DR

This paper presents a new exact black-hole solution in Einstein gravity coupled to a self-interacting scalar field, featuring scalar hair with a complex potential, supported by analytical and numerical analysis.

Contribution

It introduces a novel black-hole solution with scalar hair and a unique potential, expanding the set of known solutions in scalar-tensor gravity.

Findings

Explicit construction of a black-hole solution with scalar hair.

Analysis of a triple-well scalar potential with non-analytic minimum.

Numerical and series expansion data supporting the solution.

Abstract

Einstein gravity minimally coupled to a self-interacting scalar field is investigated in the static and isotropic situation. We explicitly construct in partially closed form a new black-hole solution with exponentially decaying scalar hair. The symmetric interaction potential has both signs and a triple-well shape with a smooth but non-analytic minimum at vanishing field. We present numerical data as well as double series expansions around spatial infinity.