Static Spherically Symmetric Solutions of Horava-Lifshitz Gravity with Projectability Condition Preserving

Inflation in general covariant Hořava-Lifshitz gravity without projectability

In this paper, we study inflation in the general covariant Hořava-Lifshitz gravity without the projectability condition. We write down explicitly the equations of the linear scalar perturbations of the FRW universe for a single scalar field without specifying to any gauge. Applying these equations to a particular gauge, we are able to obtain a master equation of the perturbations, in contrast to all the other versions of the theory without the projectability condition. This is because in the current version of the theory it has the same degree of freedom of general relativity. To calculate the…

2013-07-09astro-ph.COgr-qchep-ph

U(1) symmetry and elimination of spin-0 gravitons in Horava-Lifshitz gravity without the projectability condition

In this paper, we show that the spin-0 gravitons appearing in Horava-Lifshitz gravity without the projectability condition can be eliminated by extending the gauge symmetries of the foliation-preserving diffeomorphisms to include a local U(1) symmetry. As a result, the problems of stability, ghost, strong coupling, and different speeds in the gravitational sector are automatically resolved. In addition, with the detailed balance condition softly breaking, the number of independent coupling constants can be significantly reduced (from more than 70 down to 15), while the theory is still UV compl…

2013-01-07astro-ph.COgr-qchep-ph

General covariant Horava-Lifshitz gravity without projectability condition and its applications to cosmology

We consider an extended theory of Horava-Lifshitz gravity with the detailed balance condition softly breaking, but without the projectability condition. With the former, the number of independent coupling constants is significantly reduced. With the latter and by extending the original foliation-preserving diffeomorphism symmetry $ {Diff}(M, {\cal{F}})$ to include a local U(1) symmetry, the spin-0 gravitons are eliminated. Thus, all the problems related to them disappear, including the instability, strong coupling, and different speeds in the gravitational sector. When the theory couples to a …

2012-02-23astro-ph.COgr-qchep-th

Chiral gravitational waves from z=2 Hořava-Lifshitz gravity

We construct the chiral gravitational waves from the $z=2$ Hořava-Lifshitz gravity with gravitational Chern-Simons term in the de Sitter and Minkowski backgrounds. These gravitational waves which show a feature of the Hořava-Lifshitz gravity may be related to the generalized uncertainty principle. In addition, we find the classical and quantum IR-UV transition rules in the $z=2$ Hořava-Lifshitz gravity.

2009-12-24hep-th

Hamiltonian Analysis of Mixed Derivative Horava-Lifshitz Gravity

This short note is devoted to the canonical analysis of the Horava-Lifshitz gravity with mixed derivative terms that was proposed in arXiv:1604.04215. We determine the algebra of constraints and we show that there is one additional scalar degree of freedom with respect to the non-projectable Horava-Lifshitz gravity.

2016-07-28hep-th

Conformal Traceless Decomposition of Lagrange Multiplier Modified Horava-Lifshitz Gravity

We introduce conformal traceless decomposition in Lagrange Multiplier modified RFDiff invariant Horava-Lifshitz gravity. We perform Hamiltonian analysis of given action and determine the action for the physical degrees of freedom.

2015-02-06hep-th

On the effective potential for Horava-Lifshitz-like theories

We study the one-loop effective potential for some Horava-Lifshitz-like theories.

2012-06-22hep-th

String in Horava-Lifshitz Gravity

We generalize recent analysis of the dynamics of point particle in Horava-Lifshitz background to the case of string probe when we replace the Hamiltonian constraint of the Polyakov string with the constraint that breaks Lorentz invariance of target space-time. Then we find corresponding Lagrangian and argue that the world-sheet theory is invariant under foliation preserving diffeomorphism. Finally we discuss the Hamiltonian dynamics and show that this is well defined on condition that the world-sheet lapse function obeys the projectability condition.

2010-02-22hep-th

Holographic Superconductors in Horava-Lifshitz Gravity

We consider holographic superconductors related to the Schwarzschild black hole in the low energy limit of Hořava-Lifshitz spacetime. The non-relativistic electromagnetic and scalar fields are introduced to construct a holographic superconductor model in Hořava-Lifshitz gravity and the results show that the $α_2$ term plays an important role, modifying the conductivity curve line by means of an attenuation the conductivity.

2014-06-18hep-th

Thermodynamics of black holes in the deformed Hořava-Lifshitz gravity

We study thermodynamics of black holes in the deformed Hořava-Lifshitz gravity with coupling constant $λ$. For $λ=1$, the black hole behaves the Reissner-Norström black hole. Hence, this is different from the Schwarzschild black hole of Einstein gravity. A connection to the generalized uncertainty principle is explored to understand the Hořava-Lifshitz black holes.

2009-06-10hep-th

A note on Friedmann equation of FRW universe in deformed Horava-Lifshitz gravity from entropic force

With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann-Robertson-Walker universe for the deformed Hořava-Lifshitz gravity. It is shown that, when the parameter of Hořava-Lifshitz gravity $ω\rightarrow \infty$, the modified Friedmann equation will go back to the one in Einstein gravity. This results may imply that the entropic interpretation of gravity is effective for the deformed Hořava-Lifshitz gravity.

2011-08-31hep-th

On the gauge dependence of the effective potential for Horava-Lifshitz-like theories

We calculate the one-loop effective potential for Horava-Lifshitz-like QED with an arbitrary critical exponent within different approaches and discuss its gauge dependence.

2014-12-09hep-th

Conformally Lifshitz solutions from Horava-Lifshitz Gravity

We show that the IR action of the healthy non-projectable Hořava-Lifshitz (HL) gravity and its small modification exhibit asymptotically Lifshitz and hyperscaling violating solutions, respectively. The model may also have an AdS$_2\times R^d$ vacuum solution. By making use of our results, one may wonder that within the context of HL gravity the Lifshitz fixed point might be treated as a CFT deformed by the time component of a vector operator.

2014-10-30hep-th

Note About Hamiltonian Formalism of Modified $F(R)$ Hořava-Lifshitz Gravities and Their Healthy Extension

This note is devoted to the study of Hamiltonian formalism of modified F(R) Horava-Lifshitz theories of gravity that were proposed recently in arXiv:1001.4102[hep-th]. We also study Hamiltonian formulation of the healthy extended Horava-Lifshitz gravities and show that these theories have many unusual and interesting properties.

2010-03-02hep-th

On the z=4 Horava-Lifshitz Gravity

We consider z=4 Horava-Lifshitz gravity in both 3+1 and 4+1 dimensions. We find black hole solutions in the IR region for a kind of z=4 Horava-Lifshitz gravity which is inherited from the new massive gravity in three dimensions and an analog of the new massive gravity in four dimensions through the quantum inheritance principle. We analyze thermodynamic properties for the black hole solutions for z=4 Horava-Lifshitz gravity. We also write out the Friedmann equation in 3+1 dimensions for cosmological solutions.

2009-06-04hep-th

On the radiative corrections in the Horava-Lifshitz z=2 QED

We calculate one-loop contributions to the two and three point spinor-vector functions in z=2 Horava-Lifshitz QED. This allows us to obtain the anomalous magnetic moment.

2016-10-19hep-th

On the effective potential for Horava-Lifshitz-like theories with the arbitrary critical exponent

We calculate the one-loop effective potential for Horava-Lifshitz-like QED and Yukawa-like theory for arbitrary values of the critical exponent and the space-time dimension.

2013-01-11hep-th

Note on an action for a particle in the Hořava-Lifshitz Gravity

We reconsider a recently proposed action for a free particle which is compatible with Hořava-Lifshitz gravity, and then obtain the subluminal and the superluminal limits without gauge ambiguity in terms of Hamiltonian formulation.

2010-03-26hep-th

Dyonic solution of Horava-Lifshitz Gravity

Recently proposed Horava-Lifshitz gravity promises a UV completion of Einstein's theory by sacrificing general covariance at short distances and introducing anisotropic spacetime scaling. Here we present a dyonic solution by coupling this theory to a vector field and we discuss some properties of solution.

2009-04-28hep-th

On the Renormalizability of Horava-Lifshitz-type Gravities

In this note, we discuss the renormalizability of Horava-Lifshitz-type gravity theories. Using the fact that Horava-Lifshitz gravity is very closely related to the stochastic quantization of topologically massive gravity, we show that the renormalizability of HL gravity only depends on the renormalizability of topologically massive gravity. This is a consequence of the BRST and time-reversal symmetries pertinent to theories satisfying the detailed balance condition.

2009-05-11hep-th

Propagations of massive graviton in the deformed Hořava-Lifshitz gravity

We study massive graviton propagations of scalar, vector, and tensor modes in the deformed Hořava-Lifshitz gravity by introducing Lorentz-violating mass term. It turns out that vector and tensor modes are massively propagating on the Minkowski spacetime background. However, adding the mass term does not cure a ghost instability in the Hořava scalar.

2010-02-19hep-th

Generalized uncertainty principle and Hořava-Lifshitz gravity

We explore a connection between generalized uncertainty principle (GUP) and modified Hořava-Lifshitz (HL) gravity. The GUP density function may be replaced by the cutoff function for the renormalization group of modified Hořava-Lifshitz gravity. We find the GUP-corrected graviton propagators and compare these with tensor propagators in the HL gravity. Two are qualitatively similar, but the $p^5$-term arisen from Cotton tensor is missed in the GUP-corrected graviton propagator.

2009-08-13hep-th

Two Dimensional F(R) Horava-Lifshitz Gravity

We study two-dimensional F(R) Horava-Lifshitz gravity from the Hamiltonian point of view. We determine constraints structure with emphasis on the careful separation of the second class constraints and global first class constraints. We determine number of physical degrees of freedom and also discuss gauge fixing of the global first class constraints.

2016-11-30hep-th

Solutions in IR modified Horava-Lifshitz Gravity

In order to allow the asymptotically flat, we consider Hořava-Lifshitz gravity theory with a soft violation of the detailed balance condition and obtain various solutions. In particular, we find that such theory coupled to a global monopole leads to a solution representing a space with deficit solid angle, which is well matched with genuine feature of GR.

2010-06-09hep-th

On the Adler-Bell-Jackiw anomaly in a Horava-Lifshitz-like QED

We show the absence of the ABJ anomaly for the Horava-Lifshitz-like QED with any even $z$. Besides of this, we study the graph contributing to the ABJ anomaly at non-zero temperature and extend the Fujikawa's methodology of studying the integral measure for our model.

2015-12-28hep-th

Black holes and stars in Horava-Lifshitz theory with projectability condition

We systematically study spherically symmetric static spacetimes filled with a fluid in the Horava-Lifshitz theory of gravity with the projectability condition, but without the detailed balance. We establish that when the spacetime is spatially Ricci flat the unique vacuum solution is the de Sitter Schwarzshcild solution, while when the spacetime has a nonzero constant curvature, there exist two different vacuum solutions; one is an (Einstein) static universe, and the other is a new spacetime. This latter spacetime is maximally symmetric and not flat. We find all the perfect fluid solutions for…

2010-04-09astro-ph.COgr-qchep-th

Hamiltonian Analysis of Non-Relativistic Covariant RFDiff Horava-Lifshitz Gravity

We perform the Hamiltonian analysis of non-relativistic covariant Horava-Lifshitz gravity in the formulation presented recently in arXiv:1009.4885. We argue that the resulting Hamiltonian structure is in agreement with the original construction of non-relativistic covariant Hořava-Lifshitz gravity presented in arXiv:1007.2410. Then we extend this construction to the case of RFDiff invariant Hořava-Lifshitz theory. We find well behaved Hamiltonian system with the number of the first and the second class constraints that ensure the correct number of physical degrees of freedom of gravity.

2011-03-01hep-th

On the effective potential, Horava-Lifshitz-like theories and finite temperature

We calculate the one-loop effective potential at finite temperature for the Horava-Lifshitz-like QED and Yukawa-like theories for arbitrary values of the critical exponent and the space-time dimension. Additional remarks on the zero temperature situation are also presented.

2013-11-27hep-th

CPT-violating z=3 Horava-Lifshitz QED and generation of the Carroll-Field-Jackiw term

We study the $z=3$ Horava-Lifshitz QED with a CPT-breaking term, characterized by the axial vector $b_μ$, and perform the one-loop calculations. Explicitly, we demonstrate that just as in the usual Lorentz-breaking QED, in our case, the Carroll-Field-Jackiw term is finite but ambiguous.

2020-06-19hep-th

Note About Equivalence of F(R) and Scalar Tensor Horava-Lifshitz Gravities

In this note we study the relation between F(R) and scalar tensor Horava-Lifshitz gravity. We find that due to the broken diffeomorphism invariance corresponding scalar tensor theory has more complicated form than in case of the full diffeomorphism invariant F(R) theory of gravity. We also show that in the low energy limit this theory flows to the relativistic scalar tensor theory of gravity.

2011-08-12hep-th

On the Horava-Lifshitz-like extensions of supersymmetric theories

Within the superfield approach, we formulate two different extensions of the Wess-Zumino model and super-QED with Horava-Lifshitz-like additive terms, discuss their quantum properties and calculate lower contributions to the effective action. In the case of the gauge theory, the one-loop effective potential turns out to be gauge independent.

2014-12-02hep-th

Notes on Matter in Horava-Lifshitz Gravity

We investigate the dynamics of a scalar field governed by the Lifshitz-type action which should appear naturally in Horava-Lifshitz gravity. The wave of the scalar field may propagate with any speed without an upper bound. To preserve the causality, the action cannot have a generic form. Due to the superluminal propagation, a formation of a singularity may cause the breakdown of the predictability of the theory. To check whether such a catastrophe could occur in Horava-Lifshitz gravity, we investigate the dynamics of a dust. It turns out that the dust does not collapse completely to form a sin…

2009-12-11hep-th

Generation of Carroll-Field-Jackiw term in the Functional Integral approach within Horava-Lifshitz $z=3$ CPT-violating QED

In this paper, we apply the functional integral methodology to induce the Carroll-Field-Jackiw (CFJ) term in Horava-Lifshitz $z=3$ CPT-violating QED, where Lorentz and CPT breaking for fermion and photon sectors is introduced, and show that the CFJ term is finite but undetermined.

2021-12-07hep-th

Horava-Lifshitz Type Quantum Field Theory and Hierarchy Problem

We study the Lifshitz type extension of the standard model (SM) at UV, with dynamical critical exponent z=3. One loop radiative corrections to the Higgs mass in such a model is calculated. Our result shows that, the Hierarchy problem, which has initiated many excellent extension of the minimal SM, can be weakened in the z=3 Lifshitz type quantum field theory.

2016-06-24hep-th

Black hole solutions in Horava-Lifshitz Gravity with cubic terms

We study four dimensional non-projectable Horava-Lifshitz type gravity, in the case of an action with terms, cubic in curvature. For special choices of the free parameters of the model, we obtain two new analytic black hole solutions which exhibit the standard Schwarzschild asymptotic behavior in the large distance limit. The effect of cubic terms in the short range behavior of the black hole solutions is discussed.

2010-08-13hep-th

Holographic dark energy with varying gravitational constant in Horava-Lifshitz cosmology

We investigate the holographic dark energy scenario with a varying gravitational constant in a flat background in the context of Hořava-Lifshitz gravity. We extract the exact differential equation determining the evolution of the dark energy density parameter, which includes $G$ variation term. Also we discuss a cosmological implication of our work by evaluating the dark energy equation of state for low redshifts containing varying $G$ corrections.

2010-01-08hep-th

Lifshitz holographic superconductor in Horava-Lifshitz gravity

We study the holographic phase transition of superconductor dual to a Lifshitz black brane probed by an anisotropic scalar field in the probe limit in Hourava-Lifshitz gravity. With the use of numerical and analytical method, we investigate how the critical temperature of the condensation is affected by the Lifshitz exponent $z$, $α-$correction term in the action as well as the dimensions of the gravity. We also numerically explore the condensation of the dual operator and optical conductivity of the holographic system. Various interesting properties of the holographic condensation affected by…

2016-06-02hep-th

Horava-Lifshitz gravity and Godel Universe

We prove the consistency of the Gödel metric with the Horava-Lifshitz gravity whose action involves terms with z=1, z=2 and z=3. We show that, for different relations between the parameters of the theory, this consistency is achieved for different classes of matter, in particular, for the small cosmological constant it is achieved only for the exotic matter, that is, ghosts or phantom matter.

2011-08-02hep-th

Nonpropagation of scalar in the deformed Hořava-Lifshitz gravity

We study the propagation of a scalar, the trace of $h_{ij}$ in the deformed Hořava-Lifshitz gravity with coupling constant $λ$. It turns out that this scalar is not a propagating mode in the Minkowski spacetime background. In this work, we do not choose a gauge-fixing to identify the physical degrees of freedom and instead, make it possible by substituting the constraints into the quadratic Lagrangian.

2009-10-06hep-th

Entropy of black holes in the deformed Hořava-Lifshitz gravity

We find the entropy of Kehagias-Sfetsos black hole in the deformed Hořava-Lifshitz gravity by using the first law of thermodynamics. When applying generalized uncertainty principle (GUP) to Schwarzschild black hole, the entropy $S=A/4+(π/ω)\ln(A/4)$ may be interpreted as the GUP-inspired black hole entropy. Hence, it implies that the duality in the entropy between the Kehagias-Sfetsos black hole and GUP-inspired Schwarzschild black hole is present.

2010-01-13hep-th

Horava-Lifshitz four-fermion model revisited and dynamical symmetry breaking

In this paper, we develop studies of the dynamical symmetry breaking in the Horava-Lifshitz four-fermion model for the specific case $z=3$ and explicitly demonstrate that for various space-time dimensions, one could arrive at the theory displaying both dynamical generation of the Lorentz symmetry for the kinetic term and arising the positively defined potential at the same time. At the same time, for $D=3$, the Lorentz invariant Chern-Simons term is generated.

2019-12-31hep-th

A Trouble with Hořava-Lifshitz Gravity

We study the structure of the phase space in Hořava-Lifshitz theory. With the constraints derived from the action, the phase space is described by five fields, thus there is a lack of canonical structure. The Poisson brackets of the Hamiltonian density do not form a closed structure, resulting in many new constraints. Taking these new constraints into account, it appears that there is no degree of freedom left, or the phase space is reduced to one with an odd number of fields.

2009-08-07hep-th

Generalized uncertainty principle, quantum gravity and Hořava-Lifshitz gravity

We investigate a close connection between generalized uncertainty principle (GUP) and deformed Hořava-Lifshitz (HL) gravity. The GUP commutation relations correspond to the UV-quantum theory, while the canonical commutation relations represent the IR-quantum theory. Inspired by this UV/IR quantum mechanics, we obtain the GUP-corrected graviton propagator by introducing UV-momentum $p_i=p_{0i}(1+βp_{0}^2)$ and compare this with tensor propagators in the HL gravity. Two are the same up to $p_0^4$-order.

2009-09-29hep-th

On one-loop corrections in the Horava-Lifshitz-like QED

We study the one-loop two point functions of the gauge, scalar and spinor fields for a Horava-Lifshitz-like QED with critical exponent $z=2$. It turns out that, in certain cases, the dynamical restoration of the Lorentz symmetry at low energies can take place. We also analyze the three point vertex function of the gauge and spinor fields and prove that the triangle anomaly identically vanishes in this theory.

2015-11-23hep-th

The Friedmann equations in deformed Hořava-Lifshitz gravity and Debye model

Considering the results from Hořava-Lifshitz (HL) theory, a more precise relation between the number of bits and area in the holographic system is proposed. With this corrected relation and Debye model, two modified Friedmann equations are derived from the Hawking temperature and the Unruh temperature separately in entropic force. These equations could be better in describing the whole evolution of the universe.

2011-03-16hep-th

Fermionic Casimir effect in Horava-Lifshitz theories

In this paper, we analyze the fermionic Casimir effects associated with a massless quantum field in the context of Lorentz symmetry violation approach based on Horava-Lifshitz methodology. In order to obtain these observables, we impose the standard MIT bag boundary condition on the fields on two large and parallel plates. Our main objectives are to investigate how the Casimir energy and pressure depend on the parameter associated with the breaking of Lorentz symmetry.

2019-06-20hep-th

Comment on `Strong coupling in extended Horava-Lifshitz gravity'

We show that, contrary to the claim made in arXiv:0911.1299, the extended Horava gravity model proposed in arXiv:0909.3525 does not suffer from a strong coupling problem. By studying the observational constraints on the model we determine the bounds on the scale of the ultraviolet modification for which the proposal yields a phenomenologically viable, renormalizable and weakly coupled model of quantum gravity.

2010-02-18hep-th

Plane symmetric solutions in Horava-Lifshitz theory

The purpose of this paper is to find and analyze plane symmetric, static(non static) solutions in Hořava- Lifshitz gravity. We discussed two versions of Horava gravity. First we showed that if the detailed balance principle have considered, there are both static and non-static solutions. We show that in static case there are two family of solvable models which either of them has a well defined EOS, in analogous to the perfect fluid solutions in GR. In non-static case we find a family of solutions. Some physical properties of these solutions was discussed. Secondly we investigated the plane sym…

2010-11-14hep-th

Analysis of s-wave, p-wave and d-wave holographic superconductors in Hořava-Lifshitz gravity

In this work, the s-wave, p-wave and d-wave holographic superconductors in the Hořava-Lifshitz gravity are investigated in the probe limit. For the present approach, it is shown that the equations of motion for different wave states in Einstein gravity can be written into a unified form, and condensates take place in all three cases. This scheme is then generalized to Hořava-Lifshitz gravity, and an unified equation for multiple holographic states is obtained. Furthermore, the properties of the condensation and the optical conductivity are studied numerically. It is found that, in the case of …

2018-10-09hep-th

Hawking Radiation of Black Holes in Infrared Modified Hořava-Lifshitz Gravity

We study the Hawking radiation of the spherically symmetric, asymptotically flat black holes in the infrared modified Horava-Lifshitz gravity by applying the methods of covariant anomaly cancellation and effective action, as well as the approach of Damour-Ruffini-Sannan's. These black holes behave as the usual Schwarzschild ones of the general relativity when the radial distance is very large. We also extend the method of covariant anomaly cancellation to derive the Hawking temperature of the spherically symmetric, asymptotically AdS black holes that represent the analogues of the Schwarzschil…

2010-01-06hep-th

Note About Weyl Invariant 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.

2011-05-03gr-qchep-th

Horava-Lifshitz Gravity And Ghost Condensation

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.

2010-09-04gr-qchep-th

Lifshitz black holes in the Hořava-Lifshitz gravity

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.

2010-06-03gr-qchep-th

Remarks on "Note about Hamiltonian formalism of healthy extended Hořava-Lifshitz gravity" by J. Klusoň

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.

2011-12-29gr-qchep-th