Black string solutions with negative cosmological constant

TL;DR

This work establishes the existence of new AdS black string solutions in $d\ge 5$ with horizon topology $S^{d-3}\times S^1$ (or $H^{d-3}\times S^1$) and boundary topology $\mathbb{R}\times S^{d-3}\times \mathbb{R}$ (or $\mathbb{R}\times H^{d-3}\times \mathbb{R}$). The authors formulate the model with a negative cosmological constant, solve the static field equations numerically, and compute conserved charges via a holographic counterterm prescription, deriving a Smarr-type relation and thermodynamic quantities. They show that, upon double dimensional reduction, the reduced action possesses an exact $SL(2,R)$ symmetry, which they exploit to generate non-trivial Einstein-Maxwell-Dilaton-Liouville black holes in $(d-1)$ dimensions from the seed black strings. The results illuminate holographic aspects through the boundary stress tensor and conformal anomalies and point to extensions to AdS black rings, stability analyses, and critical phenomena in higher-dimensional gravity.

Abstract

We present arguments for the existence of new black string solutions with negative cosmological constant. These higher-dimensional configurations have no dependence on the `compact' extra dimension, and their conformal infinity is the product of time and $S^{d-3}\times R$ or $H^{d-3}\times R$. The configurations with an event horizon topology $S^{d-2}\times S^1$ have a nontrivial, globally regular limit with zero event horizon radius. We discuss the general properties of such solutions and, using a counterterm prescription, we compute their conserved charges and discuss their thermodynamics. Upon performing a dimensional reduction we prove that the reduced action has an effective $SL(2,R)$ symmetry. This symmetry is used to construct non-trivial solutions of the Einstein-Maxwell-Dilaton system with a Liouville-type potential for the dilaton in $(d-1)$-dimensions.