AdS solitons with conformal scalar hair

TL;DR

This paper investigates spherically symmetric soliton solutions in conformal gravity with a conformally coupled scalar field, revealing new limiting behaviors and differences from Einstein-Hilbert gravity related to scalar self-coupling and charge.

Contribution

It introduces new limiting behaviors of AdS solitons with scalar hair in conformal gravity and compares these to Einstein-Hilbert gravity, highlighting the role of scalar self-coupling.

Findings

Solitons interpolate between AdS vacuum and uncharged configurations.

Limiting behavior remains unchanged with scalar charge in conformal gravity.

Limiting behavior varies with scalar self-coupling.

Abstract

We study spherically symmetric soliton solutions in a model with a conformally coupled scalar field as well as in full conformal gravity. We observe that a new type of limiting behaviour appears for particular choices of the self-coupling of the scalar field, i.e. the solitons interpolate smoothly between the Anti-de Sitter vacuum and an uncharged configuration. Furthermore, within conformal gravity the qualitative approach of a limiting solution does not change when varying the charge of the scalar field - contrary to the Einstein-Hilbert case. However, it changes with the scalar self-coupling.