Lifshitz and hyperscaling violated Yang-Mills-dilaton black holes

TL;DR

This paper presents new Lifshitz and hyperscaling violating Yang-Mills-dilaton black hole solutions, analyzes their thermodynamics and stability, and explores their phase transitions in various spacetime dimensions.

Contribution

The study introduces novel black hole solutions with Lifshitz and hyperscaling violation features involving multiple gauge fields and scalar interactions, expanding the understanding of such geometries.

Findings

Solutions exist for specific Lifshitz and hyperscaling parameters.

Thermal stability depends on the dynamical exponent and spacetime dimension.

A first-order phase transition occurs at a critical temperature.

Abstract

We obtain two types of Yang-Mills-dilaton black hole solutions in both Lifshitz and hyperscaling violation spacetimes. We must consider at least three Yang-Mills gauge fields that interact with a scalar field and either $SO(n)$ or $SO(n-1,1)$ gauge symmetry groups, where $n+1$ denotes the dimension of the spacetime. They lead to the spherical and hyperbolic solutions. The obtained solutions in the hyperscaling violation spacetime fall into two categories for $z\neq n-3-\frac{n-5}{n-1}\theta$ and $z= n-3-\frac{n-5}{n-1}\theta$, where $\theta=0$ represents the Lifshitz spacetime. In order to have a real asymptotic behavior for the hyperscaling violated black hole solutions, we should consider a negative value for the hyperscaling violation parameter as $\theta<0$. We also evaluate the thermodynamic quantities of the mentioned black holes and probe their thermal stability in the grand canonical ensemble. For $z\geq2$, the hyperscaling violated solutions are not thermally stable for $z\leq n-3-\frac{n-5}{n-1}\theta$, while they are stable for large $r_{+}$ with $z>n-3-\frac{n-5}{n-1}\theta$. We also check out the critical behavior of the obtained black holes and obtain a Smarr relation for the solutions. The results also announce of a first-order small-large phase transition for both black holes in the case $T>T_{C}$.