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 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. 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., we consider a Maxwell field and a charged complex scalar field w ith the action 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 4 ψ = ψ ( r ) . (3.3) A$_{µ}$ = ( φ ( r ) , 0 , 0 , 0) , S = ∫ d $^{4}$x √ − g [ − 1 4 F$_{µν}$F µν − |∇ ψ − iA ψ | 2 − V ( | ψ | ) ] , (3.2) N 2 = f = x 2 1 − ϵ 2 − √ ϵ $^{2}$x4 + (1 − ϵ $^{2}$) xx 3 + 1 − ϵ 2 , (3.1) III. SCALAR CONDENSATION IN HO ˇ RAVA-LIFSHITZ BLACK-HOLE BACKGROUND T = √ − Λ 8 π 3 x 4 + + 2 kx 2 + − (1 − ϵ $^{2}$) k 2 x$_{+}$ ( x 2 + + (1 − ϵ $^{2}$) k ) , (2.4) ds 2 = − N $^{2}$( r ) dt 2 + dr 2 f ( r ) + r $^{2}$d Ω 2 $_{k}$, (2.2) N 2 = f = k + x 2 1 − ϵ 2 − √ ϵ $^{2}$x4 + (1 − ϵ $^{2}$) c$_{0}$x 1 − ϵ 2 , (2.3)