Thermodynamics of Rotating Charged Black Strings and (A)dS/CFT Correspondence

TL;DR

This paper investigates the thermodynamics and stability of rotating charged black strings in AdS space using the AdS/CFT correspondence, providing new insights into their conserved charges, actions, and phase stability.

Contribution

It introduces a four-dimensional Einstein-Maxwell solution with positive cosmological constant and analyzes its thermodynamic properties and stability in different ensembles.

Findings

AdS black string is locally stable in the canonical ensemble.

In the grand-canonical ensemble, stability depends on phase space region.

Calculated conserved charges and Euclidean actions for the black string.

Abstract

We use the anti-de Sitter (AdS) conformal field theory correspondence to calculate the conserved charges and the Euclidean actions of the charged rotating black string in four dimensions both in the canonical and the grand-canonical ensemble. The four-dimensional solution of the Einstein-Maxwell equations with a positive cosmological constant is introduced, and its conserved quantities and actions for fixed charge and fixed electric potential are calculated. We also study the thermodynamics of the asymptotically AdS black strings and perform a stability analysis both in the canonical and the grand-canonical ensembles. We find that the asymptotically AdS black string in the canonical ensemble is locally stable, while in the grand-canonical ensemble it is stable only for a part of the phase space.