Gravitational perturbations in the geometry of asymptotically flat black hole solution in the deformed Hořava-Lifshitz(HL) gravity are considered and the associated quasinormal mode(QNM) frequencies are evaluated using WKB method. Black holes are found to be stable against small perturbations. We also find a significant deviation in the behavior of QNMs in HL theory for low values of HL parameter $ω$, from that in the standard General Relativity(GR). QNMs are long lived in Hořava theory compared with the usual Schwarzschild black hole case.
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.
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…
We study the quasinormal modes of the massless scalar field of Park black hole in the Hořava gravity using the third order WKB approximation method and found that black hole is stable against these perturbation. We compare and discuss the results with that of Schwarzschild-de Sitter black hole. Thermodynamic properties of Park black hole are investigated and the thermodynamic behavior of upper mass bound is also studied.
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…
In this article, we study the stability of black hole solutions found in the context of dilatonic Horava-Lifshitz gravity in $1+1$ dimensions by means of the quasinormal modes approach. In order to find the corresponding quasinormal modes, we consider the perturbations of massive and massless scalar fields minimally coupled to gravity. In both cases, we found that the quasinormal modes have a discrete spectrum and are completely imaginary, which leads to damping modes. For a massive scalar field and a non-vanishing cosmological constant, our results suggest unstable behaviour for large values …
We compute the quasinormal modes (QNMs) of a massive scalar field in the background of a rotating three-dimensional Hořava AdS black hole, and we analyze the effect of the breaking of the Lorentz invariance on the QNMs. Imposing on the horizon that there are only ingoing waves and at infinity the Dirichlet boundary conditions and the Neumann boundary condition, we calculate the oscillatory and the decay modes of the QNMs. We find that the propagation of the scalar field is stable in this background and employing the holographic principle we find the different times of the perturbed system to r…
In this letter it is shown that the Horava-Lifshitz gravity theory admits Lorentz symmetry preserving preferred global time foliation of the spacetime.
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.
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 discuss the thermodynamics of the apparent horizon in $F(R)$ Hořava-Lifshitz gravity in equilibrium and non-equilibrium ensembles. We show that the second law of thermodynamics can be satisfied in this non relativistic theory.
In Horava's theory of gravity coupled to a global monopole source, we seek for static, spherically symmetric spacetime solutions for general values of $λ$. We obtain the explicit solutions with deficit solid angles, in the IR modified Horava gravity model, at the IR fixed point $λ=1$ and at the conformal point $λ=1/3$. For the other values of $1>λ>0$ we also find special solutions to the inhomogenous equation of the gravity model with detailed balance, and we discuss an possibility of astrophysical applications of the $λ=1/2$ solution that has a deficit angle for a finite range.
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.
Recently, Horava proposed a power counting renormalizable theory for (3+1)-dimensional quantum gravity, which reduces to Einstein gravity with a non-vanishing cosmological constant in IR, but possesses improved UV behaviors. In this work, we analyze the stability of the Einstein static universe by considering linear homogeneous perturbations in the context of an IR modification of Horava gravity, which implies a `soft' breaking of the `detailed balance' condition. The stability regions of the Einstein static universe are parameterized by the linear equation of state parameter w=p/ρand the para…
In this paper, we investigate the fermions Hawking radiation and quasinormal modes in infra-red modified Ho$\check{r}$ava-Lifshitz gravity under tunneling and perturbation perspectives.Firstly, through the fermions tunneling in IR modified Ho$\check{r}$ava-Lifshitz gravity,we obtain the Hawking radiation emission rate, tunneling temperature and entropy for the Kehagias-Sfetsos black hole. It is found that the results of fermions tunneling are in consistence with the thermodynamics results obtained by calculating surface gravity.Secondly, we numerically calculate the lowing quasinormal modes fr…
Recently, a field theoretic model for a UV complete theory of gravity has been proposed by Horava. This theory is a non-relativistic renormalizable gravity theory which coincides with Einstein's general relativity at large distances. Subsequently Lü et al have formulated the modified Friedmann equations and have presented a solution in vacuum. In the present work, we rewrite the modified FRW equations in the form of usual FRW equations in Einstein gravity and consequences has been analyzed. Also the thermodynamics of the FRW universe has been studied.
We investigate the area spectrum of Kehagias-Sfetsos black hole in Hořava-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 $ ΔA=4 πl_p ^2$. We have also studied the thermodynamic behavior of KS black hole by deriving different thermodynamic quantities.
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 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.
We construct a toy model for isothermal spheres in Horava gravity, which includes Einstein's gravity if a parameter is appropriately chosen. The equations for the isothermal spheres are derived from the partition function of the gravitating particle system. We confirm that the Newtonian limit of the system coincides with the model of the well-known isothermal sphere. The stability of the isothermal sphere is found to be sensitive to the energy density at the center of the sphere.
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 this paper, we have studied nonstationary radiative spherically symmetric spacetime, in general covariant theory ($U(1)$ extension) of {the} Hořava-Lifshitz gravity with the minimum coupling, in the post-newtonian approximation (PPN), without the projectability condition and in the infrared limit. The Newtonian prepotential $φ$ was assumed null. We have shown that there is not the analogue of the Vaidya's solution in the Hořava-Lifshitz Theory (HLT) with the minimum coupling, as we know in the General Relativity Theory (GRT).
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 have studied nonstationary radiative spherically symmetric spacetime, in general covariant theory ($U(1)$ extension) of Hořava-Lifshitz gravity without the projectability condition and in the infrared limit. The Newtonian prepotential $φ$ was assumed null. We have shown that there is not the analogue of the Vaidya's solution in the Hořava-Lifshitz Theory (HLT), as we know in the General Relativity Theory (GRT). Therefore, we conclude that the gauge field $A$ should interact with the null radiation field of the Vaidya's spacetime in the HLT.
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…
The Hamiltonian formulation of the lowest-order projectable Horava gravity, namely the so-called $λ$-$R$ gravity, is studied. Since a preferred foliation has been chosen in projectable Horava gravity, there is no local Hamiltonian constraint in the theory. In contrast to general relativity, the constraint algebra of $λ$-$R$ gravity forms a Lie algebra. By canonical transformations, we further obtain the connection-dynamical formalism of the $λ$-R gravity theories with real $su(2)$-connections as configuration variables. This formalism enables us to extend the scheme of non-perturbative loop qu…
We study the evolution of massive scalar field in the spacetime geometry of Kehagias-Sfetsos(KS) black hole in deformed Horava-Lifshitz(HL) gravity by numerical analysis. We find that the signature of HL theory is encoded in the quasinormal mode(QNM) phase of the evolution of field. The QNM phase in the evolution process lasts for a longer time in HL theory. QNMs involved in the evolution of massive field are calculated and find that they have a higher oscillation frequency and a lower damping rate than the Schwarzschild spacetime case. We also study the relaxation of field in the intermediate…
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 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.
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.
Recently a renormalizable model of gravity has been proposed, which might be a UV completion of General Relativity (GR) or its infra-red modification, probably with a strongly coupled scalar mode. Although the generic vacuum of the theory is anti-de Sitter one, particular limits of the theory allow for the Minkowski vacuum. In this limit (though without consideration of the strongly coupled scalar field) post-Newtonian coefficients of spherically symmetric solutions coincide with those of the General Relativity. Thus the deviations from the convenient GR should be tested beyond the post-Newton…
We reassess the conclusion by Klusoň (J. High Energy Phys. 1007 (2010) 038) that the Hamiltonian formulation of the healthy extended Hořava-Lifshitz gravity does not present any problem.
We define various Born-Infeld gravity theories in 3+1 dimensions which reduce to Horava's model at the quadratic level in small curvature expansion. In their exact forms, our actions provide z->(infinity) extensions of Horava's gravity, but when small curvature expansion is used, they reproduce finite z models, including some half-integer ones.
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 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 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 show that the Kerr metric does not exist as a fully rotating black hole solution to the modified Hořava-Lifshitz (HL) gravity with $Λ_W=0$ and $λ=1$ case. We perform it by showing that the Kerr metric does not satisfy full equations derived from the modified HL gravity.
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 present a detailed analysis of the construction of $z=2$ and $z\neq2$ scale invariant Hořava-Lifshitz gravity. The construction procedure is based on the realization of Hořava-Lifshitz gravity as the dynamical Newton-Cartan geometry as well as a non-relativistic tensor calculus in the presence of the scale symmetry. An important consequence of this method is that it provides us the necessary mechanism to distinguish the local scale invariance from the local Schrödinger invariance. Based on this result we discuss the $z=2$ scale invariant Hořava-Lifshitz gravity and the symmetry enhancement …
We investigate the Lifshitz black holes from the Hořava-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 $z=1$ Hořava black hole.
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…
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 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…
We compute the $β$-functions of marginal couplings in projectable Hořava gravity in $2+1$ spacetime dimensions. We show that the renormalization group flow has an asymptotically-free fixed point in the ultraviolet (UV), establishing the theory as a UV-complete model with dynamical gravitational degrees of freedom. Therefore, this theory may serve as a toy-model to study fundamental aspects of quantum gravity. Our results represent a step forward towards understanding the UV properties of realistic versions of Hořava 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 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 study quantum corrections to projectable Horava gravity with $z = 2$ scaling in 2+1 dimensions. Using the background field method, we utilize a non-singular gauge to compute the anomalous dimension of the cosmological constant at one loop, in a normalization adapted to the spatial curvature term.
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…
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…
Slowly rotating black holes in the non-projectable Hořava-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.
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.
Energy positivity is established for a class of solutions to Einstein-aether theory and the IR limit of Hořava gravity within a certain range of coupling parameters. The class consists of solutions where the aether 4-vector is divergence free on a spacelike surface to which it is orthogonal (which implies that the surface is maximal). In particular, this result holds for spherically symmetric solutions at a moment of time symmetry.
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 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 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.
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 …
We present interesting aspects of neutron stars (NSs) from the standpoint of a modified theory of gravity called Hořava-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.
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…
