Abstract:
We study black holes in the Ho\v{r}ava-Lifshitz gravity with a parameter $\lambda$. For $1/3 \le \lambda < 3$, the black holes behave the Lifshitz black holes with dynamical exponent $0 < z \le 4$, while for $\lambda > 3$, the black holes behave the Reissner-Nordstr\"om type black hole in asymptotically flat spacetimes. Hence, these all are quite different from the Schwarzschild-AdS black hole of Einstein gravity. The temperature, mass, entropy, and heat capacity are derived for investigating thermodynamic properties of these black holes.

Abstract:
We investigate the Lifshitz black holes from the Ho\v{r}ava-Lifshitz gravity by comparing with the Lifshitz black hole from the 3D new massive gravity. We note that these solutions all have single horizons. These black holes are very similar to each other when studying their thermodynamics. It is shown that a second order phase transition is unlikely possible to occur between $z=3,2$ Lifshitz black holes and $z=1$ Ho\v{r}ava black hole.

Abstract:
In this paper we calculate the energy distribution of the Mu-in Park, Kehagias-Sfetsos (KS) and L\"u, Mei and Pope (LMP) black holes in the Ho\v{r}ava-Lifshitz theory of gravity. These black hole solutions correspond to the standard Einstein-Hilbert action in the infrared limit. For our calculations we use the Einstein and M{\o}ller prescriptions. Various limiting and particular cases are also discussed.

Abstract:
We study the near-horizon geometry of extremal black holes in the $z=3$ Ho\v{r}ava-Lifshitz gravity with a flow parameter $\lambda$. For $\lambda>1/2$, near-horizon geometry of extremal black holes are AdS$_2 \times S^2$ with different radii, depending on the (modified) Ho\v{r}ava-Lifshitz gravity. For $1/3\le \lambda \le 1/2$, the radius $v_2$ of $S^2$ is negative, which means that the near-horizon geometry is ill-defined and the corresponding Bekenstein-Hawking entropy is zero. We show explicitly that the entropy function approach does not work for obtaining the Bekenstein-Hawking entropy of extremal black holes.

Abstract:
In the present work, we consider the possibility of observationally testing Ho\v{r}ava gravity by using the accretion disk properties around slowly rotating black holes of the Kehagias-Sfetsos solution in asymptotically flat spacetimes. The energy flux, temperature distribution, the emission spectrum as well as the energy conversion efficiency are obtained, and compared to the standard slowly rotating general relativistic Kerr solution. Comparing the mass accretion in a slowly rotating Kehagias-Sfetsos geometry in Ho\v{r}ava gravity with the one of a slowly rotating Kerr black hole, we verify that the intensity of the flux emerging from the disk surface is greater for the slowly rotating Kehagias-Sfetsos solution than for rotating black holes with the same geometrical mass and accretion rate. We also present the conversion efficiency of the accreting mass into radiation, and show that the rotating Kehagias-Sfetsos solution provides a much more efficient engine for the transformation of the accreting mass into radiation than the Kerr black holes. Thus, distinct signatures appear in the electromagnetic spectrum, leading to the possibility of directly testing Ho\v{r}ava gravity models by using astrophysical observations of the emission spectra from accretion disks.

Abstract:
We investigate the area spectrum of Kehagias-Sfetsos black hole in Ho\v{r}ava-Lifshitz gravity via modified adiabatic invariant $I=\oint p_i d q_i$ and Bohr-Sommerfeld quantization rule. We find that the area spectrum is equally spaced with a spacing of $ \Delta A=4 \pi l_p ^2$. We have also studied the thermodynamic behavior of KS black hole by deriving different thermodynamic quantities.

Abstract:
In this paper we have constructed a new class of thin-shell wormholes from black holes in Ho\v{r}ava-Lifshitz gravity. Particular emphasis is placed on those aspects that allow a comparison of Ho\v{r}ava-Lifshitz to Einstein gravity. The former enjoys a number of advantages for small values of the throat radius.

Abstract:
In this paper, we present all $[(d+1)+1]$-dimensional static diagonal vacuum solutions of the non-projectable Ho\v{r}ava-Lifshitz gravity in the IR limit, and show that they give rise to very rich Lifshitz-type structures, depending on the choice of the free parameters of the solutions. These include the Lifshitz spacetimes with or without hyperscaling violation, Lifshitz solitons, and black holes. Remarkably, even the theory breaks explicitly the Lorentz symmetry and allows generically instantaneous propagations, universal horizons still exist, which serve as one-way membranes for signals with any large velocities. In particular, particles even with infinitely large velocities would just move around on these boundaries and cannot escape to infinity. Another remarkable feature appearing in the Lifshitz-type spacetimes is that the dynamical exponent $z$ can take its values only in the ranges $1 \le z < 2$ for $d \ge 3$ and $1 \le z <\infty$ for $d = 2$, due to the stability and ghost-free conditions of the theory.

Abstract:
We study a version of the recently proposed modified $F(R)$ Ho\v{r}ava-Lifshitz gravity that abandons the projectability condition of the lapse variable. We discovered that the projectable version of this theory has a consistent Hamiltonian structure, and that the theory has interesting cosmological solutions which can describe the eras of accelerated expansion of the universe in a unified manner. The usual Ho\v{r}ava-Lifshitz gravity is a special case of our theory. Hamiltonian analysis of the non-projectable theory, however, shows that this theory has serious problems. These problems are compared with those found in the original Ho\v{r}ava-Lifshitz gravity. A general observation on the structure of the Poisson bracket of Hamiltonian constraints in all theories of the Ho\v{r}ava-Lifshitz type is made: in the resulting tertiary constraint the highest order spatial derivative of the lapse $N$ is always of uneven order. Since the vanishing of the lapse (N=0) is required by the preservation of the Hamiltonian constraints under time evolution, we conclude that the non-projectable version of the theory is physically inconsistent.

Abstract:
Slowly rotating black holes in the non-projectable Ho\v{r}ava-Lifshitz (HL) theory were studied recently in Phys. Rev. Lett. {\bf 109}, 181101 (2012), and claimed that they do not exist. In this Comment, we show that this is incorrect, and such solutions indeed exist in the IR limit of the non-projectable HL theory.