Ahmad Ghodsi
Recently a new four-dimensional non relativistic renormalizable theory of gravity was proposed by Horava. This gravity reduces to Einstein gravity at large distances. In this paper by using the new action for gravity we present different toroidal solutions to the equations of motion. Our solutions describe the near horizon geometry with slow rotating parameter.
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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.
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.
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.
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.
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.
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.
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.
We explore static spherically symmetric black hole solutions allowing a bulk U(1) vector field in the khronometric formulation of Horava gravity by way of Einstein-Aether. We examine analytic solutions and study numerical results in the limit that the khronon does not backreact on the metric.
Recently a new four-dimensional non relativistic renormalizable theory of gravity was proposed by Horava. In this paper we have found different near horizon geometries in Horava gravity. We find the rotating solutions in a special range of parameters of the theory. This range allows us to include up to six derivative terms in the equations of motion. We have found our solutions as perturbed solutions over spherical symmetric background with small rotating parameter.
This paper has been withdrawn by the authors due to the paper is far from complishment.
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.
This paper is devoted to the construction of new type of f(R) theories of gravity that are based on the principle of detailed balance. We discuss two versions of these theories with and without the projectability condition.
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.
In the present work, we search static charged black hole solutions to Hořava-Lifshitz gravity with or without projectability condition. We consider the most general form of action which electromagnetic field couples with Hořava-Lifshitz gravity. With the projectability condition, we find dS-Reissner-Nordstrom black hole solution in Painlevé-Gullstrand type coordinates in the IR region and a de-Sitter space-time solution in the UV region. Without the projectability condition, in the IR region, we find an especial static charged black hole solution.
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.
In this work we present a scalar field theory invariant under space-time anisotropic transformations with a dynamic exponet $z$. It is shown that this theory possess symmetries similar to Horava gravity and that in the limit $z=0$ the equations of motion of the non-relativistic MOND theory are obtained. This result allow us to conjecture the existence of a Horava type gravity that in the limit $z=0$ is consistent with MOND.
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.
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.
In an earlier article [arXiv:0902.0590 [hep-th], Phys. Rev D80 (2009) 025011], I discussed the potential benefits of allowing Lorentz symmetry breaking in quantum field theories. In particular I discussed the perturbative power-counting finiteness of the normal-ordered :P(phi)^{z>=d}_{d+1}: scalar quantum field theories, and sketched the implications for Horava's model of quantum gravity. In the current rather brief addendum, I will tidy up some dangling issues and fill out some of the technical details of the argument indicating the power-counting renormalizability of a z>=d variant of Horava…
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.
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.
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.
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…
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 Painlevé-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 …
Recently Horava proposed a non-relativistic renormalisable theory of gravitation, which reduces to Einstein's general relativity at large distances, and that may provide a candidate for a UV completion of Einstein's theory. In this paper, we derive the full set of equations of motion, and then we obtain spherically symmetric solutions and discuss their properties. We also obtain solutions for the Friedman-Lemaitre-Robertson-Walker cosmological metric.
We study the linearized transport of transverse momentum and charge in a conjectured field theory dual to a black brane solution of Horava gravity with Lifshitz exponent $z=1$. As expected from general hydrodynamic reasoning, we find that both of these quantities are diffusive over distance and time scales larger than the inverse temperature. We compute the diffusion constants and conductivities of transverse momentum and charge, as well the ratio of shear viscosity to entropy density, and find that they differ from their relativistic counterparts. To derive these results, we propose how the h…
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.
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.
I review the good, the bad and the ugly of the non-projectable versions of Horava gravity. I explain how this non-relativistic theory was constructed and why it was touted with such excitement as a quantum theory of gravity. I then review some of the issues facing the theory, explaining how strong coupling occurs and why this is such a problem for both phenomenology and the question of renormalisability. Finally I comment on possible violations of Equivalence Principle, and explain why these could be an issue for Blas et al's "healthy extension". This paper was presented as a talk at PASCOS 20…
In this paper we calculate the ratio of transverse shear viscosity to entropy density for the general anisotropic black brane in Horava-Lifshitz gravity. There is a well-known conjecture that states this ratio should be larger than $\frac{1}{4π}$. The ratio of shear viscosity to entropy density is proportional to the inverse square coupling of quantum thermal field theory,$\frac{η}{s} \sim \frac{1}{λ^2 }$. Especially in QFT with gravity dual the stronger coupling means the shear viscosity per entropy density gets closer to the lower bound of $\frac{1}{4π}$. The KSS bound preserves in the aniso…
We study the full spectrum of spherically symmetric solutions in the five dimensional non-projectable Horava-Lifshitz type gravity theories. For appropriate ranges of the coupling parameters, we have found several classes of solutions which are characterized by an AdS_5, dS_5 or flat large distance asymptotic behaviour, plus the standard 1/r^2 tail of the usual five-dimensional Schwarzschild black holes. In addition we have found solutions with an unconventional short or large distance behaviour, and for a special range of the coupling parameters solutions which coincide with black hole soluti…
In this note we examine whether spherically symmetric solutions in Covariant Horava Lifshitz Gravity can reproduce Newton's Law in the IR limit λ->1. We adopt the position that the auxiliary field A is independent of the space-time metric [10,11], and we assume, as in [4], that $λ$ is a running coupling constant. We show that under these assumptions, spherically symmetric solutions fail to restore the standard Newtonian physics in the IR limit λ->1, unless λdoes not run, and has the fixed value λ=1. Finally, we comment on the Horava and Melby Thompson approach [4] in which A is assumed as a pa…
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.
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.
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.
Mimetic Horava Gravity and Surface terms
本文研究拟态霍拉瓦引力，证明在拓扑为 R×Σ 的流形上，含 Gibbons-Hawking-York 表面项的引力作用量与拟态霍拉瓦作用量等价，而在其他拓扑下后者不含表面项。
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 propose an analogue of the Ryu-Takayanagi formula for holographic entanglement entropy applicable to non-relativistic holographic dualities involving Horava gravity. This is a powerful tool for the duality to have, as topological order quantified by entanglement entropy is a robust notion in condensed matter systems. Our derivation makes use of examining on-shell gravitational actions on conical spacetimes.
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 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.
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.
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.
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 …
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.
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…
In this note we search for large distance solutions of Horava gravity. In the case of the "detailed balance" action, gravity solutions asymptote to IR only above the cosmological constant ($\sim$horizon) scale. However, if one adds IR dominant terms $αR^{(3)}+βΛ_W$, one can recover general relativity solutions on usual scales in the real Universe, provided one fine-tunes the cosmological constant, reobtaining the usual cosmological constant problem. We comment on pp wave solutions, in order to gain insight into the relativistic properties of the theory.
We derive general static spherically symmetric solutions in the Horava theory of gravity with nonzero shift field. These represent "hedgehog" versions of black holes with radial "hair" arising from the shift field. For the case of the standard de Witt kinetic term (lambda =1) there is an infinity of solutions that exhibit a deformed version of reparametrization invariance away from the general relativistic limit. Special solutions also arise in the anisotropic conformal point lambda = 1/3.
In this paper we have considered the structure of the non-projectable Horava-Melby-Thompson (HMT) gravity to find braneworld scenarios. A relativistic scalar field is considered in the matter sector and we have shown how to reduce the equations of motion to first-order differential equations. In particular, we have studied thick brane solutions of both the dilatonic and Randall-Sundrum types.
We consider Horava gravity coupled to Maxwell and higher derivative magnetic terms. We construct static spherically symmetric black hole solutions in the low-energy approximation. We calculate the horizon locations and temperatures in the near-extremal limit, for asymptotically flat and (anti-)de Sitter spaces. We also construct a detailed balanced version of the theory, for which we find projectable and non-projectable, non-perturbative solutions.
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