HL Gravity Research Articles

Neutron star structure in Hořava-Lifshitz gravity

We present interesting aspects of neutron stars (NSs) from the standpoint of a modified theory of gravity called Ho\v{r}ava-Lifshitz (HL) gravity. A deviation from general relativity (GR) in HL gravity can change typical features of the NS structure. In this study, we investigate the NS structure by deriving the Tolman-Oppenheimer-Volkoff equation in HL gravity. We find that a NS in HL gravity with a larger radius and heavier mass than a NS in GR remains stable without collapsing into a black hole.

Quantum tunneling, adiabatic invariance and black hole spectroscopy

In the tunneling framework, one of us, Jiang, together with Han has studied the black hole spectroscopy via adiabatic invariance, where the adiabatic invariant quantity has been intriguingly obtained by investigating the oscillating velocity of the black hole horizon. In this paper, we attempt to improve Jiang–Han’s proposal in two ways. Firstly, we once again examine the fact that, in different types (Schwarzschild and Painlevé) of coordinates as well as in different gravity frames, the adiabatic invariant I_mathrm{adia} = oint p_i dq_i introduced by Jiang and Han is canonically invariant. Secondly, we attempt to confirm Jiang–Han’s proposal reasonably in more general gravity frames (including Einstein’s gravity, EGB gravity and HL gravity). Concurrently, for improving this proposal, we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable, but the horizon area is only an adiabatic invariant. In this sense, we emphasize the concept that the quantum of the black hole entropy is more natural than that of the horizon area.

Deformed Hořava–Lifshitz cosmology and stability of the Einstein static universe

Stability of the Einstein static universe versus the linear scalar, vector and tensor perturbations is investigated in the context of deformed Ho\v{r}ava-Lifshitz cosmology inspired by entropic force scenario. A general stability condition against the linear scalar perturbations is obtained. Using this general condition, it is shown that there is no stable Einstein static universe for the case of flat universe, $k=0$. For the the special case of large values of running parameter of HL gravity $\omega$, in a positively curved universe $k>0$, the domination of the quintessence and phantom matter fields with barotropic equation of state parameter $\beta<-\frac{1}{3}$ is necessary while for a negatively curved universe $k<0$, the matter fields with $\beta> -\frac{1}{3}$ are needed to be the dominant fields of the universe. Also, a neutral stability against the vector perturbations is obtained. Finally, an inequality including the cosmological parameters of the Einstein static universe is obtained for the stability against the tensor perturbations. It turns out that for large $\omega$ values, there is a stability against the tensor perturbations.

Effects of high-order operators in nonrelativistic Lifshitz holography

In this paper, we study the effects of high-order operators on the non-relativistic Lifshitz holography in the framework of the Ho\v{r}ava-Lifshitz (HL) theory of gravity, which naturally contains high-order operators in order for the theory to be power-counting renormalizble, and provides an ideal place for such studies. In particular, we show that the Lifshitz space-time is still a solution of the full theory of the HL gravity. The effects of the high-oder operators on the space-time itself is simply to shift the Lifshitz dynamical exponent. However, while in the infrared the asymptotic behavior of a (probe) scalar field near the boundary is similar to that studied in the literature, it gets dramatically modified in the UV limit, because of the presence of the high-order operators in this regime. Then, according to the gauge/gravity duality, this in turn affects the two-point correlation functions.

Holographic energy density on Hořava-Lifshitz cosmology

In Ho\v{r}ava-Lifshitz cosmology we use the holographic Ricci-like cut-off for the energy density proposed by L. N. Granda and A. Oliveros and under this framework we study, through the cosmic evolution at late times, the sign change in the amount of non-conservation energy ($Q$) present in this cosmology. We revise the early stage (curvature-dependent) of this cosmology, where a term reminiscent of stiff matter is the dominant, and in this stage we find a power-law solution for the cosmic scale factor although $\omega =-1$. Late and early phantom schemes are obtained without requiring $\omega <-1$. Nevertheless, these schemes are not feasible according to what is shown in this paper. We also show that $ \omega =-1$ alone does not imply a de Sitter phase in the present cosmology. Thermal aspects are revised by considering the energy interchange between the bulk and the spacetime boundary and we conclude that there is no thermal equilibrium between them. Finally, a ghost scalar graviton (extra degree of freedom in HL gravity) is required by the observational data.

Quantization of (1+1)-dimensional Hořava-Lifshitz theory of gravity

In this paper, we study the quantization of the (1+1)-dimensional projectable Ho\v{r}ava-Lifshitz (HL) gravity, and find that, when only gravity is present, the system can be quantized by following the canonical Dirac quantization, and the corresponding wavefunction is normalizable for some orderings of the operators. The corresponding Hamilton can also be written in terms of a simple harmonic oscillator, whereby the quantization can be carried out quantum mechanically in the standard way. When the HL gravity minimally couples to a scalar field, the momentum constraint is solved explicitly in the case where the fundamental variables are functions of time only. In this case, the coupled system can also be quantized by following the Dirac process, and the corresponding wavefunction is also normalizable for some particular orderings of the operators. The Hamilton can be also written in terms of two interacting harmonic oscillators. But, when the interaction is turned off, one of the harmonic oscillators has positive energy, while the other has negative energy. A remarkable feature is that orderings of the operators from a classical Hamilton to a quantum mechanical one play a fundamental role in order for the Wheeler-DeWitt equation to have nontrivial solutions. In addition, the space-time is well quantized, even when it is classically singular.

Topological charged black holes in generalized Hořava-Lifshitz gravity

As a candidate of quantum gravity in ultrahigh energy, the $(3+1)$-dimensional Ho\v{r}ava-Lifshitz (HL) gravity with critical exponent $z\ne 1$, indicates anisotropy between time and space at short distance. In the paper, we investigate the most general $z=d$ Ho\v{r}ava-Lifshitz gravity in arbitrary spatial dimension $d$, with a generic dynamical Ricci flow parameter $\lambda$ and a detailed balance violation parameter $\epsilon$. In arbitrary dimensional generalized HL$_{d+1}$ gravity with $z\ge d$ at long distance, we study the topological neutral black hole solutions with general $\lambda$ in $z=d$ HL$_{d+1}$, as well as the topological charged black holes with $\lambda=1$ in $z=d$ HL$_{d+1}$. The HL gravity in the Lagrangian formulation is adopted, while in the Hamiltonian formulation, it reduces to Dirac$-$De Witt's canonical gravity with $\lambda=1$. In particular, the topological charged black holes in $z=5$ HL$_6$, $z=4$ HL$_5$, $z=3,4$ HL$_4$ and $z=2$ HL$_3$ with $\lambda=1$ are solved. Their asymptotical behaviors near the infinite boundary and near the horizon are explored respectively. We also study the behavior of the topological black holes in the $(d+1)$-dimensional HL gravity with $U(1)$ gauge field in the zero temperature limit and finite temperature limit, respectively. Thermodynamics of the topological charged black holes with $\lambda=1$, including temperature, entropy, heat capacity, and free energy are evaluated.

Local thermodynamics of KS black hole

We study the thermodynamics of the KS black hole which is an asymptotically flat solution of the HL gravity. In particular, we introduce a cavity to describe the thermodynamics at a finite isothermal surface on general ground and to get a well-defined thermodynamics. We show that there exists a locally stable small black hole which tunnels to the hot flat space below the critical temperature and to the large black hole above the critical temperature. Moreover, it turns out that the remnant decays into the vacuum through a quantum tunneling.

Hořava-Lifshitz theory as a fermionic aether in Ashtekar gravity

We show how Ho\v{r}ava-Lifshitz (HL) theory appears naturally in the Ashtekar formulation of relativity if one postulates the existence of a fermionic field playing the role of aether. The spatial currents associated with this field must be switched off for the equivalence to work. Therefore the field supplies the preferred frame associated with breaking refoliation (time diffeomorphism) invariance, but obviously the symmetry is only spontaneously broken if the field is dynamic. When Dirac fermions couple to the gravitational field via the Ashtekar variables, the low energy limit of HL gravity, recast in the language of Ashtekar variables, naturally emerges (provided the spatial fermion current identically vanishes). HL gravity can therefore be interpreted as a time-like current, or a Fermi aether, that fills space-time, with the Immirzi parameter, a chiral fermionic coupling, and the fermionic charge density fixing the value of the parameter $\lambda$ determining HL theory. This reinterpretation sheds light on some features of HL theory, namely its good convergence properties.

Cosmology of Hořava–Lifshitz [formula omitted] gravity

We discuss the cosmology of recently proposed Hořava–Lifshitz f(R) gravity. In particular, we derive the modified Hubble equation that reduces to the standard HL gravity case in appropriate limit. We show how the bounce solutions in this theory are modified due to nonlinear effect of f(R) gravity. We also show that in principle, the Universe in this set-up can show cyclic behavior.

The absence of the Kerr black hole in the Hořava–Lifshitz gravity

We show that the Kerr metric does not exist as a fully rotating black hole solution to the modified Ho\v{r}ava-Lifshitz (HL) gravity with $\Lambda_W=0$ and $\lambda=1$ case. We perform it by showing that the Kerr metric does not satisfy full equations derived from the modified HL gravity.

Hořava-Lifshitz quantum cosmology

In this work, a minisuperspace model for the projectable Ho\v{r}ava-Lifshitz (HL) gravity without the detailed balance condition is investigated. The Wheeler-deWitt equation is derived and its solutions are studied and discussed for some particular cases where, due to HL gravity, there is a "potential barrier" nearby $a=0$. For a vanishing cosmological constant, it is found a normalizable wave function of the universe. When the cosmological constant is non-vanishing, the WKB method is used to obtain solutions for the wave function of the universe. Using the Hamilton-Jacobi equation, one discusses how the transition from quantum to classical regime occurs and, for the case of a positive cosmological constant, the scale factor is shown to grow exponentially, hence recovering the GR behaviour for the late universe.

Black strings in Hořava-Lifshitz gravity

We examine a class of cylindrically symmetric solutions in Horava-Lifshitz gravity. For the relativistic value of the coupling constant, $ \lambda=1 $, we find the "hedgehog" type static black string solution with the nonvanishing radial shift in the ADM-type decomposition of the spacetime metric. With zero radial shift, this solution corresponds to the usual BTZ black string in general relativity. However, unlike the general relativity case, the BTZ type black strings do naturally exist in HL gravity, without the need for any specific source term. We also find a rotating BTZ type black string solution which requires the nonvanishing radial shift for its very existence. We calculate the mass and the angular momentum of this solution, using the canonical Hamiltonian approach. Next, we discuss the Lemos type black string, which is inherent in general relativity with a negative cosmological constant, and present the static metric for any value of $ \lambda > 1/3 $. Finally, we show that while, for $\lambda=1 $, the entropy of the Lemos type black string is given by one quarter of the horizon area, the entropy of the static BTZ type black string is one half of its horizon area.

A new extension of Hořava-Lifshitz gravity and curing pathologies of the scalar graviton

We consider an extension of the Ho\v{r}ava-Lifshitz gravity with extra conformal symmetry by introducing a scalar field with higher order curvature terms. Relaxing the exact local Weyl symmetry, we construct an action with three free parameters which breaks local anisotropic Weyl symmetry but still preserves residual global Weyl symmetry. At low energies, it reduces to a Lorentz-violating scalar-tensor gravity. With a constant scalar field background and particular choices of the parameters, it reduces to the Ho\v{r}ava-Lifshitz (HL) gravity, but any perturbation from these particular configurations produces some non-trivial extensions of HL gravity. The perturbation analysis of the new extended HL gravity in the Minkowski background shows thatthe pathological behaviors of scalar graviton, i.e., ghost or instability problem, and strong coupling problem do not emerge up to cubic order as well as quadratic order.

Arnowitt–Deser–Misner representation and Hamiltonian analysis of covariant renormalizable gravity

We study the recently proposed Covariant Renormalizable Gravity (CRG), which aims to provide a generally covariant ultraviolet completion of general relativity. We obtain a space-time decomposed form --- an Arnowitt-Deser-Misner (ADM) representation --- of the CRG action. The action is found to contain time derivatives of the gravitational fields up to fourth order. Some ways to reduce the order of these time derivatives are considered. The resulting action is analyzed using the Hamiltonian formalism, which was originally adapted for constrained theories by Dirac. It is shown that the theory has a consistent set of constraints. It is, however, found that the theory exhibits four propagating physical degrees of freedom. This is one degree of freedom more than in Ho\v{r}ava-Lifshitz (HL) gravity and two more propagating modes than in general relativity. One extra physical degree of freedom has its origin in the higher order nature of the CRG action. The other extra propagating mode is a consequence of a projectability condition similarly as in HL gravity. Some additional gauge symmetry may need to be introduced in order to get rid of the extra gravitational degrees of freedom.

Surplus angle and sign-flipped Coulomb force in projectable Hořava-Lifshitz gravity

We obtain the static spherically symmetric vacuum solutions of Horava-Lifshitz gravity theory, imposing the detailed balance condition only in the UV limit. We find the solutions in two different coordinate systems, the Painlev\'e-Gullstrand coordinates and the Poincare coordinates, to examine the consequences of imposing the projectability condition. The solutions in two coordinate systems are distinct due to the non-relativistic nature of the HL gravity. In the Painleve-Gullstrand coordinates complying with the projectability condition, the solution involves an additional integration constant which yields surplus angle and implies attractive Coulomb force between same charges.

Smooth cosmological phase transition in the Hořava-Lifshitz gravity

We show that the cosmological phase transition from the first accelerated expansion in the early universe to the second accelerated expansion over the intermediate decelerated expansion is possible in the HL gravity without the ``detailed balance'' condition if the dark scalar energy density is assumed to be negative. Moreover, we obtain various evolutions depending on the scale factor and the expansion rate. Finally, we discuss the existence of the minimum scale in connection with the singularity free condition.

Primordial perturbation in Hořava–Lifshitz cosmology

Recently, Hořava has proposed a renormalizable theory of gravity with critical exponent z=3 in the UV. This proposal might imply that the scale invariant primordial perturbation can be generated in any expansion of early universe with a∼tn and n>1/3, which, in this Letter, will be confirmed by solving the motion equation of perturbation mode on super sound horizon scale for any background evolution of early universe. It is found that if enough efolding number of primordial perturbation suitable for observable universe is required, then n≳1 needs to be satisfied, unless the scale of UV regime is quite low. However, the possible UV completeness of HL gravity helps to relax this bound.