Phase Transitions Between Solitons and Black Holes in Asymptotically AdS/$Z_k$ Spaces

TL;DR

This paper investigates the phase transitions between solitons and black holes in asymptotically AdS/$Z_k$ spaces using thermodynamic analysis, revealing Hawking-Page and black hole-soliton transitions without smooth phase changes.

Contribution

It introduces a comprehensive thermodynamic framework for analyzing phase structures in odd-dimensional AdS/$Z_k$ spaces, including new calculations of Euclidean actions and phase transition conditions.

Findings

Hawking-Page phase transition identified

Black hole and soliton phase transition confirmed

No smooth phase transition between AdS/$Z_k$ and soliton

Abstract

We employ a thermodynamic analysis to determine the phase structure of Eguchi-Hanson solitons, Schwarzschild-AdS/$\mathbb{Z}_k$ black holes and thermal AdS/$\mathbb{Z}_k$. The Euclidean actions are calculated by two equable means: the first uses the Eguchi-Hanson soliton as the thermal background while the second makes use of minimal boundary counterterms in the action necessary to render individual actions finite. The Euclidean actions are then utilised to determine the phase structure in arbitrary odd dimension; it is found that there is a Hawking-Page phase transition and also a phase transition between the black hole and soliton. There is found to be no smooth phase transition governed by an order parameter between AdS/$\mathbb{Z}_k$ and the soliton but nevertheless AdS/$\mathbb{Z}_k$ changes phase by tunneling to the lower energy soliton configuration.