Phase Transitions in Primary Hair Planar Black Holes and Solitons

TL;DR

This paper introduces new analytic Ricci-flat black hole and soliton solutions with primary scalar hair in AdS space, analyzing their phase transitions and implications for holographic QCD models.

Contribution

It provides explicit analytic solutions for hairy black holes and solitons, and studies their phase transition behavior in the context of AdS/CFT correspondence.

Findings

First-order phase transition between hairy black hole and soliton.

Transition point depends on Euclidean time and spacelike cycle periods.

Scalar hair influences the temperature range of phase stability.

Abstract

We present a new family of Ricci-flat black hole and soliton solutions with primary scalar hair in asymptotically anti-de Sitter (AdS) space in $D$ dimensions. By solving the coupled Einstein-scalar field equations, we obtain analytic planar hairy black hole and soliton geometries. In these solutions, the scalar field and curvature scalars remain regular everywhere. We also derive analytic expressions for the mass and free energy, which indicate that the hairy soliton represents the ground state of the system. We further analyze the phase transitions between the hairy black hole and the hairy soliton, and find that there exists a first-order phase transition between them, with the transition point controlled by the ratio of the periods of Euclidean time and compact spacelike cycle. We further analyze how the scalar hair affects the transition temperature, and find that the temperature window in which the soliton phase remains preferred expands as the hair parameter increases. The hairy soliton solution obtained here is partly motivated by holographic QCD and may provide a useful gravitational background for modeling the confined phase of QCD from a bottom-up holographic perspective.