content_image/352944.jpg content_image/352945.jpg content_image/352943.jpg content_image/352941.jpg content_image/352940.jpg content_image/352939.jpg content_image/352938.jpg
can be expressed as 

with 

where x = √ − Λ r , k = − 1 , 0 , 1, and c$_{0}$ = ( x 4 $_{+}$+ 2 kx$_{+}$ + (1 − ε $^{2}$) k $^{2}$) / x$_{+}$ in which x$_{+}$ is the horizon radius of the black hole, i.e., the largest root of f ( r ) = 0. Comparing with the standard AdS$_{4}$ spacetime, we may set − Λ 1 + ϵ = 1 L 2 AdS , where L$_{AdS}$ is the radius of AdS$_{4}$. The authors in ref. [39] also found that the solutions has a finite mass M = κ $^{2}$µ2 $_{Ω$_{k}$}$√ − Λ c$_{0}$ / 16. For ϵ = 0, the solution goes back to the solution in Ref. [38]. Furthermore, when ϵ = 1, the solution becomes the (A)dS Schwarzschild black hole. 

The Hawking temperature of the black hole is 

<img src='content_image/352944.jpg'>

<img src='content_image/352945.jpg'>

<img src='content_image/352943.jpg'>

which is always a monotonically increasing function of horizon radius x$_{+}$ in the physical regime. This implies that the black holes with hyperbolic horizons in the Hoˇrava-Lifshitz theory are thermo- dynamically stable. 

## III. SCALAR CONDENSATION IN HO ˇ RAVA-LIFSHITZ BLACK-HOLE BACKGROUND 

Now, we study the scalar condensation in the Hoˇrava-Lifshi tz gravity. In the background of the black hole described by Eq. (2.3) with k = 0, i.e., 

<img src='content_image/352941.jpg'>

we consider a Maxwell field and a charged complex scalar field w ith the action 

<img src='content_image/352940.jpg'>

where F µν is the Maxwell field strength F = dA and ψ is the complex scalar field with the potential V = m $^{2}$| ψ | $^{2}$. We focus our attention on the case that these fields are weakl y coupled to gravity, i.e., they do not backreact on the metric of the spacetime. Thus, we can take the ansatz 

<img src='content_image/352939.jpg'>

<img src='content_image/352938.jpg'>

