Lifshitz and hyperscaling violated Yang-Mills-dilaton black holes

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 $T>T_{C}$.