Stability of the Einstein static universe versus the linear scalar, vector and tensor perturbations is investigated in the context of deformed Hořava-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 $ω$, in a positively curved universe $k>0$, the domination of the quintessence and phantom matter fields with barotropic equation of state parameter $β<-\frac{1}{3}$ is necessary while for a negatively curved universe $k<0$, the matter fields with $β> -\frac{1}{3}$ 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 $ω$ values, there is a stability against the tensor perturbations.
In this letter it is shown that the Horava-Lifshitz gravity theory admits Lorentz symmetry preserving preferred global time foliation of the spacetime.
We study z=4 Topological black hole in 4+1 dimensional Horava-Lifshitz gravity and we calculate analytically the quasinormal modes of scalar perturbations and from these quasinormal modes we show that z=4 Topological black hole in 4+1 dimensional Horava-Lifshitz gravity is stable.
Classical and quantum Friedmann-Lemaître-Robertson-Walker universes filled with non-interacting radiation and dust fluids are considered in the framework of Hořava-Lifshitz gravity theory. The Hořava-Lifshitz theory is set in its projectable version and without detailed balance condition. Canonical quantization is performed in the Wheeler-DeWitt approach of quantum cosmology for a minisuperspace model in the light of de Broglie-Bohm interpretation of quantum mechanics. The main results are analytical solutions for non-singular quantum bounce and cyclic universes for open and closed spatial sec…
In this paper we have constructed a new class of thin-shell wormholes from black holes in Hořava-Lifshitz gravity. Particular emphasis is placed on those aspects that allow a comparison of Hořava-Lifshitz to Einstein gravity. The former enjoys a number of advantages for small values of the throat radius.
The effects of Horava-Lifshitz corrections to the gravito-magnetic field are analyzed. Solutions in the weak field, slow motion limit, referring to the motion of a satellite around the Earth are considered. The post-newtonian paradigm is used to evaluate constraints on the Horava-Lifshitz parameter space from current satellite and terrestrial experiments data. In particular, we focus on GRAVITY PROBE B, LAGEOS and the more recent LARES mission, as well as a forthcoming terrestrial project, GINGER.
We investigate the Hawking radiation of 3+1 and 4+1 dimensional black holes in the $z = 4$ Horava-Lifshitz gravity with fermion tunnelling. It turns out that the Hawking temperatures are recovered and are in consistence with those obtained by calculating surface gravity of the black holes. For the 3+1 dimensional black holes, the Hawking temperatures are related to the fundamental parameters of Horava-Lifshitz gravity.
In this paper, we investigate the scalar quasinormal modes of Hořava-Lifshitz theory with $U(1)$ symmetry in static Anti-de Sitter spacetime. The static planar and spherical black hole solutions in lower energy limit are derived in non-projectable Hořava-Lifshitz gravity. The equation of motion of a scalar field is obtained, and is utilized to study the quasinormal modes of massless scalar particles. We find that the effect of Hořava-Lifshitz correction is to increase the quasinormal period as well as to slow down the decay of the oscillation magnitude. Besides, the scalar field could be unsta…
In this paper we calculate the energy distribution of the Mu-in Park, Kehagias-Sfetsos (KS) and Lü, Mei and Pope (LMP) black holes in the Hořava-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 Møller prescriptions. Various limiting and particular cases are also discussed.
The z=3 deformed Horava-Lifshitz gravity with coupling constants ωand εleads to a nonrelativistic "mixmaster" cosmological model. The potential of theory is given by the sum of IR and UV potentials in the ADM Hamiltonian formalism. It turns out that the presence of the UV-potential cannot suppress chaotic behaviors existing in the IR-potential, which comes from curvature anisotropy.
We study the entropy of black holes in the deformed Horava-Lifshitz gravity with coupling constant lambda. For lambda=1, the black hole resembles the Reissner-Norstrom black hole with a geometric parameter acting like the electric charge. Therefore, we obtain some differences in the entropy when comparing with the Schwarzschild black hole. Finally, we study the heat capacity and the thermodynamical stability of this solution.
In this short note we clarify a link between anisotropic-scaling scenarios and Finsler spacetimes. Generalizing earlier analysis it is shown that the kinematics of propagating particles (in the sense of geometrical optics) can be described in terms of (pseudo-)Finsler structures.
Non-stationary null dust in a spherically symmetric spacetime is studied in the context of a general-covariant Horava-Lifshitz theory. The non-minimal coupling to matter is considered in the infrared limit. The aim of this paper is to study whether the collapse of a null dust-like fluid can be a solution of Hořava-Lifshitz theory in the infrared limit. We have shown that the unique possible solution is static. This solution represents a Minkowski spacetime since the energy density is null.
In this letter, we have considered generalized Ricci dark energy in the Horava-Lifshitz gravity. We have reconstructed the Hubble's parameter in terms of fractional densities. We have viewed the equation of state parameter in this situation. Also, we have examined the behavior of deceleration parameter and investigated the nature of the statefinder diagnostics. The equation of state parameter has exhibited quintessence-like behavior and from the plot of the deceleration parameter we have observed an ever accelerating universe.
Analytical solutions of Maxwell equations around black hole immersed in external uniform magnetic field in the background of the Kehagias-Sfetsos (KS) asymptotically flat black hole solution of Hořava-Lifshitz gravity have been found. Influence of magnetic field on effective potential of the radial motion of charged test particle around black hole immersed in external magnetic field in Hořava-Lifshitz gravity has been investigated by using Hamilton-Jacobi method. Exact analytical solution for dependence of the minimal radius of the circular orbits $r_{\rm mc}$ from KS parameter $ω$ for motion …
In the present paper we consider the possibility of observationally testing Horava gravity at the scale of the Solar System, by considering the classical tests of general relativity (perihelion precession of the planet Mercury, deflection of light by the Sun and the radar echo delay) for the Kehagias-Sfetsos asymptotically flat black hole solution of Horava-Lifshitz gravity. All these gravitational effects can be fully explained in the framework of the vacuum solution of Horava gravity, and it is shown that the analysis of the classical general relativistic tests severely constrain the free pa…
In the present letter, we consider the DeBroglie-Bohm interpretation of a Hořava-Lifshitz quantum cosmology model in the presence of a radiation perfect fluid. We compute the Bohm's trajectories for the scale factor and show that it never goes to zero. That result gives a strong indication that this model is free from singularities, at the quantum level. We also compute the quantum potential. That quantity helps understanding why the scale factor never vanishes.
We construct Horava-Lifshitz gravities that are invariant under anisotropic Weyl scaling. This construction is based on an extension of the group of symmetries of healthy extended Horava-Lifshitz gravity and RFDiff invariant Horava-Lifshitz gravity. We find their Hamiltonian formulation and determine their constraint structure.
Inspired by Lifshitz theory for quantum critical phenomena in condensed matter, Horava proposed a theory for quantum gravity with an anisotropic scaling in ultraviolet. In Horava-Lifshitz gravity (HLG), we have studied the impacts of six types of equations of state on the evolution of various cosmological parameters such as Hubble parameters and scale factor. From the comparison of the general relativity gravity with the HLG with detailed and without with non-detailed balance conditions, remarkable differences are found. Also, a noticeable dependence of singular and non-singular Big Bang on th…
In this work were studied quantum models of a Friedmann-Robertson-Walker (FRW) cosmology in the framework of the gravity's theory proposed by Hořava, the so-called Hořava-Lifshitz theory of the gravity. It was used the Hořava theory for the projectable Hořava-Lifshitz (HL) gravity without the detailed balance condition. Following the quantization of the model in the context of Wheeler-DeWitt approach and taking in account the ordering factor for operators were found the cosmological wave function. Solutions were studied and the results were discussed for some particular cases close of initial …
In this paper we formulate RFDiff invariant f(R) Horava-Lifshitz gravity and we show that it is related to the ghost condensation in the projectable version of Horava-Lifshitz gravity.
Penrose process on rotational energy extraction of the black hole (BH) in the original non-projectable Hořava-Lifshitz gravity is studied. The strong dependence of the extracted energy from the special range of parameters of the Hořava-Lifshitz gravity, such as parameter $Λ_W$ and specific angular momentum $a$ has been found. Particle acceleration near the rotating BH in Hořava-Lifshitz gravity has been studied. It is shown that the fundamental parameter of the Hořava-Lifshitz gravity can impose limitation on the the energy of the accelerating particles preventing them from the infinite value.
We study the quasinormal modes of the massless scalar perturbation in the background of a deformed black hole in the Hořava-Lifshitz gravity with coupling constant $λ=1$. Our results show that the quasinormal frequencies depend on the parameter in the Hořava-Lifshitz gravity and the behavior of the quasinormal modes is different from those in the Reissner-Norstr\"{om} and Einstein-Born-Infeld black hole spacetimes. The absolute value of imaginary parts is smaller and the scalar perturbations decay more slowly in the deformed Hořava-Lifshitz black hole spacetime. This information can help us un…
We consider RFDiff invariant Horava-Lifshitz gravity action with additional Lagrange multiplier term that is a function of scalar curvature. We find its Hamiltonian formulation and we show that the constraint structure implies the same number of physical degrees of freedom as in General Relativity.
In this work, we have considered Cardassian Universe in Horava-Lifshitz gravity. Four types of Cardassian Universe models i.e., polytropic/power law, modified polytropic, exponential and modified exponential models have been considered for accelerating models. The natures of statefinder parameters, deceleration parameter, Om diagnostic and EoS parameters have been investigated for all types of Cardassian models in Horava-Lifshitz gravity.
We argue that the true nature of the renormalizability of Horava-Lifshitz gravity lies in the presence of higher order spatial derivatives and not in the anisotropic Lifshitz scaling of space and time. We discuss the possibility of constructing a higher order spatial derivatives model that has the same renormalization properties of Horava-Lifshitz gravity but that does not make use of the Lifshitz scaling. In addition, the state-of-the-art of the Lorentz symmetry restoration in Horava-Lifshitz-type theories of gravitation is reviewed.
We study the dynamical evolution of a massless scalar perturbation in the Hořava-Lifshitz black-hole spacetimes with the coupling constants $λ={1/3}$, $λ={1/2}$ and $λ=3$, respectively. Our calculation shows that, for the three cases, the scalar perturbations decay without any oscillation in which the decay rate imprints the parameter of the Hořava-Lifshitz black hole. The results are quite different from those in the Schwarzschild AdS black hole and can help us understand more about the Hořava-Lifshitz gravity.
We derive the projectable version of Horava - Lifshitz gravity from the localisation of the Galilean symmetry. Specifically we provide a dynamical construction of the metric, from first principles, that reproduces the transformations of the physical variables - lapse, shift and spatial component of the metric. Also, the measure defining the action is reproduced. The geometrical basis of the Horava-Lifshitz gravity is thereby revealed which also elucidates its difference from the Newton-Cartan geometry - the spacetime of Newtonian gravity. The connection of Newton's gravity with Horava-Lifshitz…
Horava-Lifshitz gravity with "detailed balance" but without the projectability assumption is discussed. It is shown that detailed balance is quite efficient in limiting the proliferation of couplings in Horava-Lifshitz gravity, and that its implementation without the projectability assumption leads to a theory with sensible dynamics. However, the (bare) cosmological constant is restricted to be large and negative.
We derive the detailed balance condition as a solution to the Hamilton-Jacobi equation in the Horava-Lifshitz gravity. This result leads us to propose the existence of the d-dimensional quantum field theory on the future boundary of the (d+1)-dimensional Horava-Lifshitz gravity from the viewpoint of the holographic renormalization group. We also obtain a Ricci flow equation of the boundary theory as the holographic RG flow, which is the Hamilton equation in the bulk gravity, by tuning parameters in the theory.
In this paper we continue the study of the Hamiltonian formalism of the healthy extended Horava-Lifshitz gravity. We find the constraint structure of given theory and argue that this is the theory with the second class constraints. Then we discuss physical consequence of this result. We also apply the Batalin-Tyutin formalism of the conversion of the system with the second class constraints to the system with the first class constraints to the case of the healthy extended Horava-Lifshitz theory. As a result we find new theory of gravity with structure that is different from the standard formul…
We discuss some aspects of the Horava-Lifshitz cosmology with different matter components considered as dominants at different stages of the cosmic evolution (each stage is represented by an equation of state pressure/density=constant). We compare cosmological solutions from this theory with their counterparts of General Relativity (Friedmann cosmology). At early times, the Horava- Lifshitz cosmology contains a curvature-dependent dominant term which is stiff matter-reminiscent and this fact motivates to discuss, in some detail, this term beside the usual stiff matter component (pressure=densi…
We use the Wetterich equation for foliated spacetimes to study the RG flow of projectable Horava-Lifshitz gravity coupled to n Lifshitz scalars. Using novel results for anisotropic heat kernels, the matter-induced beta functions for the gravitational couplings are computed explicitly. The RG flow exhibits an UV attractive anisotropic Gaussian fixed point where Newton's constant vanishes and the extra scalar mode decouples. This fixed point ensures that the theory is asymptotically free in the large-n expansion, indicating that projectable Horava-Lifshitz gravity is perturbatively renormalizabl…
We quantize the two-dimensional projectable Horava-Lifshitz gravity with a bi-local as well as space-like wormhole interaction. The resulting quantum Hamiltonian coincides with the one obtained through summing over all genus in the string field theory for two-dimensional causal dynamical triangulations. This implies that our wormhole interaction can be interpreted as a splitting or joining interaction of one-dimensional strings.
We investigate the connection between Gravity's Rainbow and Horava-Lifshitz gravity, since both theories incorporate a modification in the UltraViolet regime which improves their quantum behavior at the cost of the Lorentz invariance loss. In particular, extracting the Wheeler-De Witt equations of the two theories in the case of Friedmann-Lemaitre-Robertson-Walker and spherically symmetric geometries, we establish a correspondence that bridges them.
We show that certain three-dimensional Horava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various non-relativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schroedinger algebra each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Horava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Horava-Lifshitz gravity with a local U(1) gauge symmetry without (with) a cosmological …
Using the multiplicity of solutions for the projectable case of the covariant extension of Horava-Lifshitz Gravity, we show that an appropriate choice for the auxiliary field allows for an effective description of galaxy rotation curves. This description is based on static and spherically symmetric solutions of covariant Horava-Lifshitz Gravity and does not require Dark Matter.
We find topological (charged) black holes whose horizon has an arbitrary constant scalar curvature $2k$ in Hořava-Lifshitz theory. Without loss of generality, one may take $k=1,0$ and -1. The black hole solution is asymptotically AdS with a nonstandard asymptotic behavior. Using the Hamiltonian approach, we define a finite mass associated with the solution. We discuss the thermodynamics of the topological black holes and find that the black hole entropy has a logarithmic term in addition to an area term. We find a duality in Hawking temperature between topological black holes in Hořava-Lifshit…
Approximately one year ago Horava proposed a power-counting renormalizable theory of gravity which abandons local Lorentz invariance. The proposal has been received with growing interest and resulted in various different versions of Horava-Lifshitz gravity theories, involving a colourful potpourri of new terminology. In this proceedings contribution we first motivate and briefly overview the various different approaches, clarifying their differences and similarities. We then focus on a model referred to as projectable Horava-Lifshitz gravity and summarize the key results regarding its viabilit…
We investigate slowly rotating black holes in the Hořava-Lifshitz (HL) gravity. For $Λ_W=0$ and $λ=1$, we find a slowly rotating black hole of the Kehagias-Sfetsos solution in asymptotically flat spacetimes. We discuss their thermodynamic properties by computing mass, temperature, angular momentum, and angular velocity on the horizon.
When the cosmological constant is non-zero the dynamics of the cosmological model based on Horava-Lifshitz gravity in a non-flat universe is characterized by using the qualitative theory of differential equations.
We formulate Horava-Lifshitz cosmology with an additional scalar field that leads to an effective dark energy sector. We find that, due to the inherited features from the gravitational background, Horava-Lifshitz dark energy naturally presents very interesting behaviors, possessing a varying equation-of-state parameter, exhibiting phantom behavior and allowing for a realization of the phantom divide crossing. In addition, Horava-Lifshitz dark energy guarantees for a bounce at small scale factors and it may trigger the turnaround at large scale factors, leading naturally to cyclic cosmology.
We look for a Brans-Dicke type of generalization of the Horava-Lifshitz gravity. It is shown that such a generalization is possible within the detailed balance condition. Classically, the resulting theory reduces in the IR limit to the usual Brans-Dicke theory with a negative cosmological constant for certain values of parameters. We then consider homogeneous and isotropic cosmology and study the effects of the new terms appearing in the model.
In this paper we show that by considering a slightly modified Horava-Lifshitz gravity one can find self-tuning cosmological scenarios. Since in the proposed model the cosmological constant cancels out, then regardless of its value it cannot produce any gravitational effect. As a consequence this removes the gravitational effect of the vacuum energy on the expansion of the Universe. Accelerating scenarios, however, can be found through the presence of conventional and non-conventional fluids.
Using the qualitative theory of differential equations, the global dynamics of a cosmological model based on Horava-Lifshitz gravity is studied in the space with zero curvature in the presence of the non-zero cosmological constant.
In this paper we focus on the Halmiton-Jacobi method to determine several thermodynamic quantities such as the temperature, entropy and specific heat of two-dimensional Horava-Lifshitz black holes by using the generalized uncertainty principles (GUP). We also address the product of horizons, mainly concerning the event, Cauchy, cosmological and virtual horizons.
The anti--de Sitter/conformal field theory (AdS/CFT) correspondence is a powerful tool that promises to provide new insights toward a full understanding of field theories under extreme conditions, including but not limited to quark-gluon plasma, Fermi liquid and superconductor. In many such applications, one typically models the field theory with asymptotically AdS black holes. These black holes are subjected to stringy effects that might render them unstable. Hořava-Lifshitz gravity, in which space and time undergo different transformations, has attracted attentions due to its power-counting …
The occurrence of a bounce in the FRW cosmology requires modifications of General Relativity. An example of such a modification is the recently proposed Horava-Lifshitz theory of gravity, which includes a "dark radiation" term with a negative coefficient in the analog of the Friedmann equation. A modification of the HL gravity, relaxing the "detailed balance" condition, brings additional terms to the equations of motion, corresponding to stiff matter. This paper presents comparison of the phase structure of the original and modified Horava cosmology. Special attention is paid to the analysis o…
Causal Dynamical Triangulations (CDT) is a lattice theory where aspects of quantum gravity can be studied. Two-dimensional CDT can be solved analytically and the continuum (quantum) Hamiltonian obtained. In this article we show that this continuum Hamiltonian is the one obtained by quantizing two-dimensional projectable Horava-Lifshitz gravity.
In this paper we investigate the physical implications of the dynamical scalar mode in pure Horava-Lifshitz gravity on cosmology. We find that it can produce a scale-invariant power spectrum in UV era if the detailed balance condition on the action is relaxed. This indicates that the physical scalar mode may seed the large scale structure and Horava-Lifshitz cosmology could be a qualified alternative to inflationary scenario.
In this paper we address the issue of black hole solutions in (1+1)-dimensional non-projectable Horava-Lifshitz gravity. We consider several models by considering different potentials in the scalar matter sector. We also consider the gravitational collapse of a distribution of pressureless dust filling a region in one-dimensional space. The time of the collapse can be faster or slower depending on the parameter $λ$ of the theory.
An extension of Horava-Lifshitz gravity was recently proposed in order to address the pathological behavior of the scalar mode all previous versions of the theory exhibit. We show that even in this new extension the strong coupling persists, casting doubts on whether such a model can constitute an interesting alternative to general relativity (GR).
We investigate the Gauss-Bonnet dark energy model and its deformed version on Hořava-Lifshitz cosmology, which belongs to the class of cosmologies obtained from the so-called projectable version of Hořava-Lifshitz gravity. In particular, we investigate the bulk/boundary interaction in this scenario through the $Q$ function, which we interpret as a measure of the energy transference between the bulk and the spacetime boundary. Then we discuss whether the thermal equilibrium will be stable or not, once it is reached, and the validity of the generalized second law. We show that the $Q$ function c…
We study asymptotically Lifshitz solutions with critical exponent $z \neq 1$ in Horava gravity in three and four spacetime dimensions. For $z=2$ and $z=3/2$, we find a novel class of numerical solutions with regular universal horizon, but are characterized by non-analytic behavior near infinity. In the interior, inside the universal horizon, the unit timelike vector field associated with the preferred time foliation exhibits oscillatory behavior, qualitatively similar to that found earlier in asymptotically flat solutions. For $z>2$ no solutions of this type appear to exist. We comment on pote…
We investigate string-like solutions in four dimensions based on Hořava-Lifshitz gravity. For a restricted class of solutions where the Cotton tensor vanishes, we find that the string-like solutions in Einstein gravity including the BTZ black strings are solutions in Hořava-Lifshitz gravity as well. The geometry is warped in the same way as in Einstein gravity, but the "conformal" lapse function is not constrained in Hořava-Lifshitz gravity. It turns out that if $λ\ne 1$, there exist no other solutions. For the value of model parameter with which Einstein gravity recovers in IR limit (i.e., $λ…
In this paper we calculate the center-of-mass energy of two colliding test particles near the rotating and non-rotating Horava-Lifshitz black hole. For the case of slowly rotating KS solution of Horava-Lifshitz black hole we compare our results with the case of Kerr black holes. We confirm the limited value of the center-of-mass energy for the static black holes and unlimited value of the center-of-mass energy for the rotating black holes. Numerically, we discuss temperature dependence of the center-of-mass energy on the black hole horizon. We obtain the critical angular momentum of particles.…
In this work, some new integrable and nonintegrable cosmological models of the Ho$\check{r}$ava-Lifshitz gravity are proposed. For some of them, exact solutions are presented. Then these results extend for the F(R) Ho$\check{r}$ava-Lifshitz gravity theory case. In particular, several integrable cosmological models of this modified gravity theory were constructed in the explicit form.
It is well known that by applying the first law of thermodynamics to the apparent horizon of a Friedmann-Robertson-Walker universe, one can derive the corresponding Friedmann equations in Einstein, Gauss-Bonnet, and more general Lovelock gravity. Is this a generic feature of any gravitational theory? Is the prescription applicable to other gravities? In this paper we would like to address the above questions by examining the same procedure for Horava-Lifshitz gravity. We find that in Horava-Lifshitz gravity, this approach does not work and we fail to reproduce a corresponding Friedmann equatio…
This paper is intended to study diffeomorphism invariance and diffeomorphism generation in the modified theory of gravity proposed by Horava. Firstly, we demonstrate that the theory does not lose diffeomorphism invariance due to the parameter $λ$, as it was previously believed. However, we show that the presence of terms containing the Levi-Civita symbol in the original proposal of Horava makes the theory diffeomorphism dependent. By neglecting such terms, what returns fully diffeomorphism invariance to the action, we obtain the equations of motion. Secondly, in the Hamiltonian formalism, we c…
The cosmological equations suggested by the non-relativistic renormalizable gravitational theory proposed by Hořava are considered. It is pointed out that the early universe cosmology has features that may give an alternative to inflation and the theory may be able to escape singularities.
